diff --git a/lib/addmagma.gi b/lib/addmagma.gi
index 72f692d91b7..ab653cbf46e 100644
--- a/lib/addmagma.gi
+++ b/lib/addmagma.gi
@@ -175,7 +175,7 @@ InstallGlobalFunction( SubadditiveMagmaNC, function( M, gens )
     if IsEmpty( gens ) then
       K:= NewType( FamilyObj(M),
                        IsAdditiveMagma
-                   and IsTrivial
+                   and IsEmpty
                    and IsAttributeStoringRep );
       S:= Objectify( K, rec() );
       SetGeneratorsOfAdditiveMagma( S, [] );
diff --git a/lib/magma.gd b/lib/magma.gd
index d939bcd6207..e8615ed42b2 100644
--- a/lib/magma.gd
+++ b/lib/magma.gd
@@ -129,8 +129,13 @@ DeclareCategory( "IsMagmaWithInverses",
         IsMagmaWithInversesIfNonzero
     and IsMultiplicativeElementWithInverseCollection );
 
+# FIXME: this is wrong for empty magmas
+# InstallTrueMethod( IsMagmaWithInverses,
+#     IsFiniteOrderElementCollection and IsMagma );
+
 InstallTrueMethod( IsMagmaWithInverses,
-    IsFiniteOrderElementCollection and IsMagma );
+    IsFiniteOrderElementCollection and IsMagmaWithOne );
+
 
 #############################################################################
 ##
diff --git a/tst/testbugfix/2018-05-09-submagma.tst b/tst/testbugfix/2018-05-09-submagma.tst
new file mode 100644
index 00000000000..4566649ae19
--- /dev/null
+++ b/tst/testbugfix/2018-05-09-submagma.tst
@@ -0,0 +1,54 @@
+#
+# There was a bug where we marked a sub additive magma
+# with empty generator list as trivial, even though it is empty.
+#
+# There was also a wrong implication, from "IsFiniteOrderElementCollection and
+# IsMagma" to IsMagmaWithInverses. But a collection with the former filters may
+# be empty, and then it isn't a IsMagmaWithInverses.
+#
+gap> amgm:=AdditiveMagma([0]);
+<additive magma with 1 generators>
+gap> Size(amgm);
+1
+gap> IsTrivial(amgm);
+true
+gap> IsEmpty(amgm);
+false
+gap> IsMagmaWithInverses(amgm);
+false
+
+#
+gap> asub:=SubadditiveMagma(amgm, []);
+<additive magma with 0 generators>
+gap> Size(asub);
+0
+gap> IsTrivial(asub);
+false
+gap> IsEmpty(asub);
+true
+gap> IsMagmaWithInverses(asub);
+false
+
+#
+gap> mgm:=Magma( () );
+<commutative semigroup with 1 generator>
+gap> Size(mgm);
+1
+gap> IsTrivial(mgm);
+true
+gap> IsEmpty(mgm);
+false
+gap> IsMagmaWithInverses(mgm);
+false
+
+#
+gap> sub:=Submagma(mgm,[]);
+<commutative semigroup with 0 generators>
+gap> Size(sub);
+0
+gap> IsTrivial(sub);
+false
+gap> IsEmpty(sub);
+true
+gap> IsMagmaWithInverses(sub);
+false