diff --git a/doc/container.qbk b/doc/container.qbk
index a87742d..9528e83 100644
--- a/doc/container.qbk
+++ b/doc/container.qbk
@@ -1252,6 +1252,7 @@ use [*Boost.Container]? There are several reasons for that:
 * Fixed serious bug in heterogeneous lookup functions (is_transparent was broken).
 
 * Fixed bugs:
+   * [@https://github.com/boostorg/container/issues/79 GitHub #79: ['"Mark small_vector move operations noexcept"]].
    * [@https://github.com/boostorg/container/issues/82 GitHub #82: ['"Function definition in header file"]].
    * [@https://github.com/boostorg/container/issues/83 GitHub #83: ['"Iterator zero incrementing leads to assert on empty vector"]].
    * [@https://github.com/boostorg/container/pull/85   GitHub #85: ['"container: misc-typos"]].
diff --git a/include/boost/container/small_vector.hpp b/include/boost/container/small_vector.hpp
index 6f5c050..c0edac8 100644
--- a/include/boost/container/small_vector.hpp
+++ b/include/boost/container/small_vector.hpp
@@ -608,6 +608,7 @@ class small_vector : public small_vector_base<T, Allocator>
    {  this->move_construct_impl(other, other.get_stored_allocator());   }
 
    BOOST_CONTAINER_FORCEINLINE small_vector(BOOST_RV_REF(small_vector) other)
+      BOOST_NOEXCEPT_IF(boost::container::dtl::is_nothrow_move_assignable<value_type>::value)
       : base_type(initial_capacity_t(), internal_capacity(), ::boost::move(other.get_stored_allocator()))
    {  this->move_construct_impl(other, other.get_stored_allocator());   }
 
@@ -627,6 +628,9 @@ class small_vector : public small_vector_base<T, Allocator>
    {  return static_cast<small_vector&>(this->base_type::operator=(static_cast<base_type const&>(other)));  }
 
    BOOST_CONTAINER_FORCEINLINE small_vector& operator=(BOOST_RV_REF(small_vector) other)
+      BOOST_NOEXCEPT_IF(boost::container::dtl::is_nothrow_move_assignable<value_type>::value
+         && (allocator_traits_type::propagate_on_container_move_assignment::value
+             || allocator_traits_type::is_always_equal::value))
    {  return static_cast<small_vector&>(this->base_type::operator=(BOOST_MOVE_BASE(base_type, other))); }
 
    BOOST_CONTAINER_FORCEINLINE small_vector& operator=(const base_type &other)
diff --git a/include/boost/container/static_vector.hpp b/include/boost/container/static_vector.hpp
index f230763..059640e 100644
--- a/include/boost/container/static_vector.hpp
+++ b/include/boost/container/static_vector.hpp
@@ -372,6 +372,7 @@ public:
     //! @par Complexity
     //!   Linear O(N).
     BOOST_CONTAINER_FORCEINLINE static_vector & operator=(BOOST_RV_REF(static_vector) other)
+       BOOST_NOEXCEPT_IF(boost::container::dtl::is_nothrow_move_assignable<value_type>::value)
     {
         return static_cast<static_vector&>(base_t::operator=(BOOST_MOVE_BASE(base_t, other)));
     }