In the paper the notion of the conceptual model of a programming language is proposed. This formalism represents types of the programming language, values, exceptions, states and executable constructs of the abstract machine of the language, and the constraints for these entities at the conceptual level. The new definition of conceptual transition systems oriented to specification of conceptual models of programming languages is presented, the language of redefined conceptual transition systems CTSL is described, and the technique of the use of CTSL as a domain-specific language of specification of conceptual models of programming languages is proposed. The conceptual models for the family of sample programming languages illustrate this technique.