diff --git a/src/variable.jl b/src/variable.jl
index b5230f07b..4e7f23adb 100644
--- a/src/variable.jl
+++ b/src/variable.jl
@@ -503,21 +503,29 @@ function SymbolicIndexingInterface.symbolic_evaluate(ex::Union{Num, Arr, Symboli
 end
 
 """
-    fixpoint_sub(expr, dict; operator = Nothing)
+    fixpoint_sub(expr, dict; operator = Nothing, maxiters = 10000)
 
 Given a symbolic expression, equation or inequality `expr` perform the substitutions in
 `dict` recursively until the expression does not change. Substitutions that depend on one
 another will thus be recursively expanded. For example,
 `fixpoint_sub(x, Dict(x => y, y => 3))` will return `3`. The `operator` keyword can be
-specified to prevent substitution of expressions inside operators of the given type.
+specified to prevent substitution of expressions inside operators of the given type. The
+`maxiters` keyword is used to limit the number of times the substitution can occur to avoid
+infinite loops in cases where the substitutions in `dict` are circular
+(e.g. `[x => y, y => x]`).
 
 See also: [`fast_substitute`](@ref).
 """
-function fixpoint_sub(x, dict; operator = Nothing)
+function fixpoint_sub(x, dict; operator = Nothing, maxiters = 10000)
     y = fast_substitute(x, dict; operator)
-    while !isequal(x, y)
+    while !isequal(x, y) && maxiters > 0
         y = x
         x = fast_substitute(y, dict; operator)
+        maxiters -= 1
+    end
+
+    if !isequal(x, y)
+        @warn "Did not converge after `maxiters = $maxiters` substitutions. Either there is a cycle in the rules or `maxiters` needs to be higher."
     end
 
     return x
diff --git a/test/utils.jl b/test/utils.jl
index 616dee642..977bed6b9 100644
--- a/test/utils.jl
+++ b/test/utils.jl
@@ -38,3 +38,11 @@ end
     @test var_from_nested_derivative(p) == (p, 0)
     @test var_from_nested_derivative(D(p(x))) == (p(x), 1)
 end
+
+@testset "fixpoint_sub maxiters" begin
+    @variables x y
+    expr = Symbolics.fixpoint_sub(x, Dict(x => y, y => x))
+    @test isequal(expr, x)
+    expr = Symbolics.fixpoint_sub(x, Dict(x => y, y => x); maxiters = 9)
+    @test isequal(expr, y)
+end