diff --git a/test/usecases/nonlinear/nonlin.mod b/test/usecases/nonlinear/nonlin.mod
new file mode 100644
index 000000000..ec0bed30f
--- /dev/null
+++ b/test/usecases/nonlinear/nonlin.mod
@@ -0,0 +1,21 @@
+NEURON {
+    SUFFIX nonlin
+}
+
+STATE { x }
+
+FUNCTION solve() {
+    : Iterative solvers need a starting guess.
+    x = 1.0
+    SOLVE eq
+
+    solve = x
+}
+
+NONLINEAR eq {
+    ~ x*x = 4.0
+}
+
+FUNCTION residual(x) {
+    residual = x - 2.0
+}
diff --git a/test/usecases/nonlinear/test_nonlin.py b/test/usecases/nonlinear/test_nonlin.py
new file mode 100644
index 000000000..eef75edbd
--- /dev/null
+++ b/test/usecases/nonlinear/test_nonlin.py
@@ -0,0 +1,15 @@
+from neuron import h, gui
+
+
+def test_nonlin():
+    s = h.Section()
+    s.insert("nonlin")
+    inst = s(0.5).nonlin
+
+    x = inst.solve()
+    error = inst.residual(x)
+    assert abs(error) < 1e-9, f"{x = }, {error = }"
+
+
+if __name__ == "__main__":
+    test_nonlin()