In this paper, we introduce a class of substructural logics, called normal substructural logics, which includes not only relevant logic, BCK logic, linear logic and the Lambek calculus but also weak logics with strict implication, and de ne Kripke- style semantics (Kripke frames and models) for normal substructural logics. Then we show a correspondence between axioms and properties on frames, and give a canonical construction of Kripke models for normal substructural logics. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.