In this paper we pursue the study of the variety L-n(m) of m-generalized Lukasiewicz algebras of order n which was initiated in . This variety contains the variety of Lukasiewicz algebras of order n. Given A is an element of L-n(m), we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Lukasiewicz algebra of order n and for each congruence on A we find a description via the corresponding Stone filter. We characterize the principal congruences on A via Stone filters. In doing so, we obtain a polynomial equation which defines the principal congruences on the algebras of L-n(m). After showing that for m > 1 and n > 2, the variety of Lukasiewicz algebras of order n is a proper subvariety of L-n(m), we prove that L-n(m) is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability.