This paper develops a semantical model - theoretic account of (logical) content complementing the syntactically specified account of content developed in "A New Theory of Content I", JPL 23: 596-620, 1994. Proofs of Completeness are given for both propositional and quantificational languages (without identity). Means for handling a quantificational language with identity are also explored. Finally, this new notion of content is compared, in respect of both logical properties and philosophical applications, to alternative partitions of the standard consequence class relation (...) proposed by Stelzner, Schurz and Wiengartner. (shrink)