diff --git a/include/boost/multiprecision/float128.hpp b/include/boost/multiprecision/float128.hpp
index cd70fa00..43416723 100644
--- a/include/boost/multiprecision/float128.hpp
+++ b/include/boost/multiprecision/float128.hpp
@@ -144,10 +144,10 @@ public:
       return *this;
    }
    template <class T>
-   BOOST_CONSTEXPR float128_backend(const T& i, const typename enable_if_c<is_convertible<T, float128_type>::value>::type* = 0) BOOST_NOEXCEPT
+   BOOST_CONSTEXPR float128_backend(const T& i, const typename enable_if_c<is_convertible<T, float128_type>::value>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval<float128_type&>() = std::declval<const T&>()))
       : m_value(i) {}
    template <class T>
-   typename enable_if_c<is_arithmetic<T>::value || is_convertible<T, float128_type>::value, float128_backend&>::type operator = (const T& i) BOOST_NOEXCEPT
+   typename enable_if_c<is_arithmetic<T>::value || is_convertible<T, float128_type>::value, float128_backend&>::type operator = (const T& i) BOOST_NOEXCEPT_IF(noexcept(std::declval<float128_type&>() = std::declval<const T&>()))
    {
       m_value = i;
       return *this;
diff --git a/test/test_nothrow_float128.cpp b/test/test_nothrow_float128.cpp
index c41678e3..6b377f55 100644
--- a/test/test_nothrow_float128.cpp
+++ b/test/test_nothrow_float128.cpp
@@ -48,6 +48,31 @@ BOOST_STATIC_ASSERT(boost::has_nothrow_copy<boost::multiprecision::float128>::va
 BOOST_STATIC_ASSERT(boost::has_nothrow_assign<boost::multiprecision::float128>::value);
 #endif
 
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128()));
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128(std::declval<const boost::multiprecision::float128&>())));
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128(std::declval<boost::multiprecision::float128>())));
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128(std::declval<const float128_type&>())));
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128(std::declval<float128_type>())));
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128(std::declval<const double&>())));
+BOOST_STATIC_ASSERT(noexcept(boost::multiprecision::float128(std::declval<double>())));
+BOOST_STATIC_ASSERT(noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<const boost::multiprecision::float128&>()));
+BOOST_STATIC_ASSERT(noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<boost::multiprecision::float128>()));
+BOOST_STATIC_ASSERT(noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<const float128_type&>()));
+BOOST_STATIC_ASSERT(noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<float128_type>()));
+BOOST_STATIC_ASSERT(noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<const double&>()));
+BOOST_STATIC_ASSERT(noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<double>()));
+
+struct any_convert
+{
+   template <class T>
+   operator T ()const;   // Can throw!
+};
+
+BOOST_STATIC_ASSERT(!noexcept(boost::multiprecision::float128(std::declval<const any_convert&>())));
+BOOST_STATIC_ASSERT(!noexcept(boost::multiprecision::float128(std::declval<any_convert>())));
+BOOST_STATIC_ASSERT(!noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<const any_convert&>()));
+BOOST_STATIC_ASSERT(!noexcept(std::declval<boost::multiprecision::float128&>() = std::declval<any_convert>()));
+
 #endif // noexcept