diff --git a/src/Bridges/NonlinearBridge.jl b/src/Bridges/NonlinearBridge.jl
index 7363d1f..7fbaa83 100644
--- a/src/Bridges/NonlinearBridge.jl
+++ b/src/Bridges/NonlinearBridge.jl
@@ -29,7 +29,11 @@ The relaxation method is determined by the
 ## Target nodes
 
 `NonlinearBridge` creates nonlinear constraints depending on the relaxation
-method (for example, quadratic or `ScalarNonlinearFunction` constraints).
+method:
+
+  * [`MOI.ScalarQuadraticFunction{T}`](@ref) in [`MOI.LessThan{T}`](@ref)
+  * [`MOI.ScalarQuadraticFunction{T}`](@ref) in [`MOI.GreaterThan{T}`](@ref)
+  * [`MOI.ScalarNonlinearFunction`](@ref) in [`MOI.LessThan{T}`](@ref)
 """
 mutable struct NonlinearBridge{T,S} <: MOI.Bridges.Constraint.AbstractBridge
     constraints::Vector
@@ -100,8 +104,21 @@ function MOI.Bridges.added_constrained_variable_types(::Type{<:NonlinearBridge})
     return Tuple{Type}[]
 end
 
-function MOI.Bridges.added_constraint_types(::Type{<:NonlinearBridge})
-    return Tuple{Type,Type}[]
+function MOI.Bridges.added_constraint_types(
+    ::Type{<:NonlinearBridge{T}},
+) where {T}
+    # The reformulation produces, depending on the relaxation method:
+    #  * `ScalarQuadraticFunction`-in-`LessThan` (Scholtes, Liu-Fukushima)
+    #  * `ScalarQuadraticFunction`-in-`GreaterThan` (Liu-Fukushima)
+    #  * `ScalarNonlinearFunction`-in-`LessThan`
+    #    (Fischer-Burmeister, Kanzow-Schwarz)
+    # Since the relaxation is an instance attribute and not part of the bridge
+    # type, we declare the union of all the constraint types that may be added.
+    return Tuple{Type,Type}[
+        (MOI.ScalarQuadraticFunction{T}, MOI.LessThan{T}),
+        (MOI.ScalarQuadraticFunction{T}, MOI.GreaterThan{T}),
+        (MOI.ScalarNonlinearFunction, MOI.LessThan{T}),
+    ]
 end
 
 function MOI.get(
diff --git a/test/Bridges/test_NonlinearBridge.jl b/test/Bridges/test_NonlinearBridge.jl
index 579514a..f58d693 100644
--- a/test/Bridges/test_NonlinearBridge.jl
+++ b/test/Bridges/test_NonlinearBridge.jl
@@ -230,6 +230,63 @@ function test_KS_Nonpositives_with_unbounded_x1()
     return
 end
 
+# `MOI.Bridges.runtests` cannot catch an under-specified
+# `added_constraint_types`: its `_general_bridge_tests` only iterates over the
+# *declared* types to check consistency, so it never verifies that every
+# constraint actually added by the bridge is declared. We check that here
+# explicitly for each relaxation, since the produced constraint types depend on
+# the relaxation (quadratic for Scholtes/Liu-Fukushima, nonlinear for
+# Fischer-Burmeister/Kanzow-Schwarz).
+function _test_added_constraint_types(relax)
+    T = Float64
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{T}())
+    B = MathOptComplements.Bridges.NonlinearBridge{T}
+    model = MOI.Bridges.Constraint.SingleBridgeOptimizer{B}(inner)
+    x1 = MOI.add_variable(model)
+    x2, _ = MOI.add_constrained_variable(model, MOI.GreaterThan(zero(T)))
+    ci = MOI.add_constraint(
+        model,
+        MOI.VectorOfVariables([x1, x2]),
+        MathOptComplements.ComplementsWithSetType{MOI.Nonnegatives}(2),
+    )
+    if relax !== nothing
+        MOI.set(
+            model,
+            MathOptComplements.ComplementarityReformulation(),
+            ci,
+            relax,
+        )
+    end
+    MOI.Bridges.final_touch(model)
+    CB = MathOptComplements.Bridges.NonlinearBridge{T,MOI.Nonnegatives}
+    # The bridge adds no variable, so `added_constrained_variable_types` is
+    # empty.
+    @test isempty(MOI.Bridges.added_constrained_variable_types(CB))
+    declared = MOI.Bridges.added_constraint_types(CB)
+    for (F, S) in MOI.get(inner, MOI.ListOfConstraintTypesPresent())
+        # The bound on `x2` is added by the test, not by the bridge.
+        if F == MOI.VariableIndex
+            continue
+        end
+        @test (F, S) in declared
+    end
+    return
+end
+
+function test_added_constraint_types()
+    _test_added_constraint_types(nothing)  # ScholtesRelaxation (the default)
+    _test_added_constraint_types(
+        MathOptComplements.FischerBurmeisterRelaxation(1e-8),
+    )
+    _test_added_constraint_types(
+        MathOptComplements.LiuFukushimaRelaxation(1e-8),
+    )
+    _test_added_constraint_types(
+        MathOptComplements.KanzowSchwarzRelaxation(1e-8),
+    )
+    return
+end
+
 function test_Zeros_equality()
     MOI.Bridges.runtests(
         MathOptComplements.Bridges.NonlinearBridge,