diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index 2c1526b07..176c78452 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -16,12 +16,16 @@ NonlinearSolveBase = {path = "../NonlinearSolveBase"}
 
 [weakdeps]
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
 
 [extensions]
 BracketingNonlinearSolveForwardDiffExt = "ForwardDiff"
+BracketingNonlinearSolveChainRulesCoreExt = ["ChainRulesCore", "ForwardDiff"]
 
 [compat]
 Aqua = "0.8.9"
+ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 ExplicitImports = "1.10.1"
@@ -34,6 +38,7 @@ SciMLBase = "2.69"
 Test = "1.10"
 TestItemRunner = "1"
 julia = "1.10"
+Zygote = "0.6.69, 0.7"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
@@ -42,6 +47,7 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "ExplicitImports", "ForwardDiff", "InteractiveUtils", "Test", "TestItemRunner"]
+test = ["Aqua", "ExplicitImports", "ForwardDiff", "InteractiveUtils", "Test", "TestItemRunner", "Zygote"]
diff --git a/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveChainRulesCoreExt.jl b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveChainRulesCoreExt.jl
new file mode 100644
index 000000000..388517367
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveChainRulesCoreExt.jl
@@ -0,0 +1,34 @@
+module BracketingNonlinearSolveChainRulesCoreExt
+
+using BracketingNonlinearSolve: bracketingnonlinear_solve_up, CommonSolve, SciMLBase
+using CommonSolve: solve
+using SciMLBase: IntervalNonlinearProblem
+using ForwardDiff
+using ChainRulesCore: ChainRulesCore, AbstractThunk, NoTangent, Tangent, unthunk
+
+function ChainRulesCore.rrule(
+        ::typeof(bracketingnonlinear_solve_up),
+        prob::IntervalNonlinearProblem,
+        sensealg, p, alg, args...; kwargs...
+)
+    out = solve(prob, alg)
+    u = out.u
+    f = SciMLBase.unwrapped_f(prob.f)
+    function ∇bracketingnonlinear_solve_up(Δ)
+        Δ = Δ isa AbstractThunk ? unthunk(Δ) : Δ
+        # Δ = dg/du
+        Δ isa Tangent ? delu = Δ.u : delu = Δ
+        λ = only(ForwardDiff.derivative(u -> f(u, p), only(u)) \ delu)
+        if p isa Number
+            dgdp = -λ * ForwardDiff.derivative(p -> f(u, p), p)
+        else
+            dgdp = -λ * ForwardDiff.gradient(p -> f(u, p), p)
+        end
+        return (NoTangent(), NoTangent(), NoTangent(),
+            dgdp, NoTangent(),
+            ntuple(_ -> NoTangent(), length(args))...)
+    end
+    return out, ∇bracketingnonlinear_solve_up
+end
+
+end
\ No newline at end of file
diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
index 64db84621..9337ac6fe 100644
--- a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -24,10 +24,22 @@ include("ridder.jl")
 function CommonSolve.solve(prob::IntervalNonlinearProblem; kwargs...)
     return CommonSolve.solve(prob, ITP(); kwargs...)
 end
+
 function CommonSolve.solve(prob::IntervalNonlinearProblem, nothing, args...; kwargs...)
     return CommonSolve.solve(prob, ITP(), args...; kwargs...)
 end
 
+function CommonSolve.solve(prob::IntervalNonlinearProblem, 
+        alg::AbstractBracketingAlgorithm, args...; sensealg = nothing, kwargs...)
+    return bracketingnonlinear_solve_up(prob::IntervalNonlinearProblem, sensealg, prob.p, alg, args...; kwargs...)
+end
+
+
+function bracketingnonlinear_solve_up(prob::IntervalNonlinearProblem, sensealg, p, alg, args...; kwargs...)
+    return SciMLBase.__solve(prob, alg, args...; kwargs...)
+end
+
+
 @setup_workload begin
     for T in (Float32, Float64)
         prob_brack = IntervalNonlinearProblem{false}(
diff --git a/lib/BracketingNonlinearSolve/src/alefeld.jl b/lib/BracketingNonlinearSolve/src/alefeld.jl
index 6880f8c95..86807986a 100644
--- a/lib/BracketingNonlinearSolve/src/alefeld.jl
+++ b/lib/BracketingNonlinearSolve/src/alefeld.jl
@@ -8,7 +8,7 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 """
 struct Alefeld <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(
+function SciMLBase.__solve(
         prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         maxiters = 1000, abstol = nothing, kwargs...
 )
diff --git a/lib/BracketingNonlinearSolve/src/bisection.jl b/lib/BracketingNonlinearSolve/src/bisection.jl
index 91c17a775..5f056abbc 100644
--- a/lib/BracketingNonlinearSolve/src/bisection.jl
+++ b/lib/BracketingNonlinearSolve/src/bisection.jl
@@ -19,7 +19,7 @@ A common bisection method.
     exact_right::Bool = false
 end
 
-function CommonSolve.solve(
+function SciMLBase.__solve(
         prob::IntervalNonlinearProblem, alg::Bisection, args...;
         maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
 )
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
index 7baebc90c..6199bf29a 100644
--- a/lib/BracketingNonlinearSolve/src/brent.jl
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -5,7 +5,7 @@ Left non-allocating Brent method.
 """
 struct Brent <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(
+function SciMLBase.__solve(
         prob::IntervalNonlinearProblem, alg::Brent, args...;
         maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
 )
diff --git a/lib/BracketingNonlinearSolve/src/falsi.jl b/lib/BracketingNonlinearSolve/src/falsi.jl
index 3074a5eb4..a2bdbde1f 100644
--- a/lib/BracketingNonlinearSolve/src/falsi.jl
+++ b/lib/BracketingNonlinearSolve/src/falsi.jl
@@ -5,7 +5,7 @@ A non-allocating regula falsi method.
 """
 struct Falsi <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(
+function SciMLBase.__solve(
         prob::IntervalNonlinearProblem, alg::Falsi, args...;
         maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
 )
diff --git a/lib/BracketingNonlinearSolve/src/itp.jl b/lib/BracketingNonlinearSolve/src/itp.jl
index cbf5818bf..c733dc25f 100644
--- a/lib/BracketingNonlinearSolve/src/itp.jl
+++ b/lib/BracketingNonlinearSolve/src/itp.jl
@@ -56,7 +56,7 @@ function ITP(; scaled_k1::Real = 0.2, k2::Real = 2, n0::Int = 10)
     return ITP(scaled_k1, k2, n0)
 end
 
-function CommonSolve.solve(
+function SciMLBase.__solve(
         prob::IntervalNonlinearProblem, alg::ITP, args...;
         maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
 )
diff --git a/lib/BracketingNonlinearSolve/src/muller.jl b/lib/BracketingNonlinearSolve/src/muller.jl
index 7b89236a0..1e321969b 100644
--- a/lib/BracketingNonlinearSolve/src/muller.jl
+++ b/lib/BracketingNonlinearSolve/src/muller.jl
@@ -27,7 +27,7 @@ end
 
 Muller() = Muller(nothing)
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Muller, args...;
+function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Muller, args...;
         abstol = nothing, maxiters = 1000, kwargs...)
     @assert !SciMLBase.isinplace(prob) "`Muller` only supports out-of-place problems."
     xᵢ₋₂, xᵢ = prob.tspan
diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
index 9192897c5..9e38d25b6 100644
--- a/lib/BracketingNonlinearSolve/src/ridder.jl
+++ b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -5,7 +5,7 @@ A non-allocating ridder method.
 """
 struct Ridder <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(
+function SciMLBase.__solve(
         prob::IntervalNonlinearProblem, alg::Ridder, args...;
         maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
 )
diff --git a/lib/BracketingNonlinearSolve/test/adjoint_tests.jl b/lib/BracketingNonlinearSolve/test/adjoint_tests.jl
new file mode 100644
index 000000000..50c2dce2a
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/test/adjoint_tests.jl
@@ -0,0 +1,18 @@
+@testitem "Simple Adjoint Test" tags=[:adjoint] begin
+    using ForwardDiff, Zygote, BracketingNonlinearSolve
+
+    ff(u, p) = u^2 .- p[1]
+
+    function solve_nlprob(p)
+        prob = IntervalNonlinearProblem{false}(ff, (1.0, 3.0), p)
+        sol = solve(prob, Bisection())
+        res = sol isa AbstractArray ? sol : sol.u
+        return sum(abs2, res)
+    end
+
+    p = [2.0, 2.0]
+
+    ∂p_zygote = only(Zygote.gradient(solve_nlprob, p))
+    ∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
+    @test ∂p_zygote ≈ ∂p_forwarddiff
+end