The author continues his work on difference families in additive Abelian groups of finite orders [For earlier works see Mat. Sb., Nov. Ser. 99(141), 366-379 (1976; Zbl 0405.05010), and Mat. Zametki 32, No.6, 869- 887 (1982; Zbl 0506.05011)]. The present paper contains many interesting construction theorems. Only two of them will be quoted (Theorems 1 and 2). Let G be an additive Abelian group of order v. A family \({\mathfrak F}\) of k- subsets B of G is called a difference family with parameters (v,k,\(\lambda)\) if \(\sum_{a\neq b,a,b\in B\in {\mathfrak F}}a-b=\lambda (G- \{0\})\) (in the group ring Z(G) of G over the ring of rational integers). Moreover if there exist cycle forms of B's such that for any j, \(1\leq j\leq k-1\), \(\sum_{a,b\in B\in {\mathfrak F},\quad \rho (a,b)=j}a-b=G- \{0\},\) where \(\rho\) denotes the natural distance in cycles, then \(\lambda =k-1\) and \({\mathfrak F}\) is called a T(v,k,k-1) difference family in G. Here if G-\(\{\) \(0\}\) is replaced by \(\mu\) (G-\(\{\) \(0\})\), \({\mathfrak F}\) is called a \(T_{\mu}(v,k,k-1)\) difference family in G. Furthermore if for any nonzero g in G there exist exactly m B's containing g, \({\mathfrak F}\) is called a \(\tilde T_{\mu}(v,k,k-1)\) family in G. Now the results can be stated. (1) Assume that there exist a (v,k,\(\lambda)\) difference family in G and a \(T_{\mu}(k,k_ 1,k_ 1- 1)\) difference family in an additive Abelian group of order k. Then there exists a \(T_{\lambda \mu}(v,k_ 1,k_ 1-1)\) difference family in G. (2) Assume that there exist a \(\tilde T_{\mu}(v,k,k-1)\) difference family in G and a \(\tilde T_{\nu}(w,k,k-1)\) difference family in an additive Abelian group G' of order w, then there exists a \(\tilde T_{\mu \nu}(vw,k,k-1)\) difference family in \(G\times G'\).