Subgroups, congruences and normal subgroups are investigated for-groups. These are latticevalued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal ?-subgroup is defined as a particular class in an ?-congruence. Our main result is that the quotient groups over cuts of a normal ?-subgroup of an ?-group G?, are classical normal subgroups of the corresponding quotient groups over G?. We also describe the minimal normal ?-subgroup of an ?-group, and some other constructions related to ?-valued congruences.