A general approach is suggested to revise axiomatics of connectives in fuzzy logic. The study is carried out by solving functional equations for conjunctions. Then, starting from a t-norm, new families of fuzzy conjunctions and implications are introduced. Those t-norms are completely characterized for which R-implications and S-implications defined by any conjunction of the family coincide. This study is carried out by solving a functional equation for t-norms, providing a new characterization of the Hamacher's family of t-norms. >