In a previous paper, [Des., Codes and Cryptogr.8(1996), 215–227]; we used Galois rings to construct partial difference sets, relative difference sets and a difference set. In the present paper, we first generalize and improve the construction of partial difference sets in [Des., Codes and Cryptogr.8(1996), 215–227]; also we obtain a family of relative difference sets from these partial difference sets. Second, we construct a class of relative difference sets in (Z 4 ) 2m+1 ⊕(Z 4 ) r ⊕(Z 2 ⊕Z 2 ) s ,r+s=m, r, s⩾0 with respect to a subgroup (Z 2 ) 2m+1 . These constructions make use of character sums from Galois rings, and relate relative difference sets to Hadamard difference sets.