diff --git a/doc/mp11/algorithm.adoc b/doc/mp11/algorithm.adoc
index ab31f52..1326fc3 100644
--- a/doc/mp11/algorithm.adoc
+++ b/doc/mp11/algorithm.adoc
@@ -262,7 +262,8 @@ Same as `mp_repeat_c` but with a type argument `N`. The number of copies is `N::
 
 `mp_product<F, L1<T1...>, L2<T2...>, ..., Ln<Tn...>>` evaluates `F<U1, U2, ..., Un>` for values `Ui` taken from
 the Cartesian product of the lists, as if the elements `Ui` are formed by `n` nested loops, each traversing `Li`.
-It returns a list of the form `L1<V...>` containing the results of the application of `F`.
+It returns a list of the form `L1<V...>` containing the results of the application of `F`. The degenerate case
+of zero lists, `mp_product<F>`, returns `mp_list<F<>>`.
 
 .mp_product on two lists
 [cols="<.^4m,4*^.^1m",width=85%]
diff --git a/include/boost/mp11/algorithm.hpp b/include/boost/mp11/algorithm.hpp
index f0a700d..73a15e7 100644
--- a/include/boost/mp11/algorithm.hpp
+++ b/include/boost/mp11/algorithm.hpp
@@ -254,7 +254,9 @@ template<class L, class N> using mp_repeat = typename detail::mp_repeat_c_impl<L
 namespace detail
 {
 
-template<template<class...> class F, class P, class... L> struct mp_product_impl_2;
+template<template<class...> class F, class P, class... L> struct mp_product_impl_2
+{
+};
 
 template<template<class...> class F, class P> struct mp_product_impl_2<F, P>
 {
@@ -266,7 +268,14 @@ template<template<class...> class F, class P, template<class...> class L1, class
     using type = mp_append<typename mp_product_impl_2<F, mp_push_back<P, T1>, L...>::type...>;
 };
 
-template<template<class...> class F, class... L> struct mp_product_impl;
+template<template<class...> class F, class... L> struct mp_product_impl
+{
+};
+
+template<template<class...> class F> struct mp_product_impl<F>
+{
+    using type = mp_list< F<> >;
+};
 
 template<template<class...> class F, class L1, class... L> struct mp_product_impl<F, L1, L...>
 {
diff --git a/test/mp_product.cpp b/test/mp_product.cpp
index 3d3d2ad..f00bc40 100644
--- a/test/mp_product.cpp
+++ b/test/mp_product.cpp
@@ -24,9 +24,10 @@ struct Y1 {};
 struct Z1 {};
 struct Z2 {};
 
-template<class T1, class T2, class T3> struct F {};
-
 template<class T> struct F1 {};
+template<class T1, class T2, class T3> struct F3 {};
+
+template<class...> struct F {};
 
 int main()
 {
@@ -40,8 +41,8 @@ int main()
         using L2 = mp_list<Y1>;
         using L3 = std::pair<Z1, Z2>;
 
-        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product<F, L1, L2, L3>, std::tuple<F<X1, Y1, Z1>, F<X1, Y1, Z2>, F<X2, Y1, Z1>, F<X2, Y1, Z2>, F<X3, Y1, Z1>, F<X3, Y1, Z2>>>));
-        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product_q<mp_quote<F>, L1, L2, L3>, std::tuple<F<X1, Y1, Z1>, F<X1, Y1, Z2>, F<X2, Y1, Z1>, F<X2, Y1, Z2>, F<X3, Y1, Z1>, F<X3, Y1, Z2>>>));
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product<F3, L1, L2, L3>, std::tuple<F3<X1, Y1, Z1>, F3<X1, Y1, Z2>, F3<X2, Y1, Z1>, F3<X2, Y1, Z2>, F3<X3, Y1, Z1>, F3<X3, Y1, Z2>>>));
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product_q<mp_quote<F3>, L1, L2, L3>, std::tuple<F3<X1, Y1, Z1>, F3<X1, Y1, Z2>, F3<X2, Y1, Z1>, F3<X2, Y1, Z2>, F3<X3, Y1, Z1>, F3<X3, Y1, Z2>>>));
     }
 
     {
@@ -49,8 +50,8 @@ int main()
         using L2 = mp_list<>;
         using L3 = std::pair<Z1, Z2>;
 
-        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product<F, L1, L2, L3>, std::tuple<>>));
-        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product_q<mp_quote<F>, L1, L2, L3>, std::tuple<>>));
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product<F3, L1, L2, L3>, std::tuple<>>));
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product_q<mp_quote<F3>, L1, L2, L3>, std::tuple<>>));
     }
 
     {
@@ -64,5 +65,10 @@ int main()
         BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product_q<mp_quote<F1>, L2>, mp_list<F1<X1>, F1<X2>, F1<X3>>>));
     }
 
+    {
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product<F>, mp_list<F<>>>));
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_product_q<mp_quote<F>>, mp_list<F<>>>));
+    }
+
     return boost::report_errors();
 }