In this paper, " non-Fregean logics " proposed by R. Suszko are studied ; 1. from a philosophical point of view concerning the necessity of introducing the identity-connective, and 2. from technical point of view concerning logical structure of non-Fregean logics. Analysing the Frege's ambiguity in treating the logical constants 1,0 (in Frege), we were led to the conclusion ; 1) A distinction between valuational two valuedness and ontological (referential) two-valuedness should be made, 2) keeping the valuational two-valuedness (the principle of bivalence), the abolition of ontological one is possible (ontological many-valuedness), 3) in order to express logical systems based on valuational two-valuedness and ontological many-valuedness, the introduction of identity-connective is unavoidable. Such logics have been studied among others by R. Suszko as theories of kind W, and its sentential part is called SCI (sentential calculus with identity). In this paper, our interest was directed esp. on 1) logical relations between SCI, SC (sentential calculus) and there intermediate variaties, 2) A possibility of introducing some meta-notions into object languages, 3) some valuations of non-Fregean languages.