In the paper the notion of the conceptual operational semantics of a programming language is proposed. This formalism represents operational semantics of a programming language in terms of its conceptual model based on conceptual transition systems. The special kind of conceptual transition systems, operational conceptual transition systems, oriented to specification of conceptual operational semantics of programming languages is defined, the extension of the language of conceptual transition systems CTSL for operational conceptual transition systems is described, and the technique of the use of the extended CTSL as a domain-specific language of specification of conceptual operational semantics of programming languages is proposed. The conceptual operational semantics for the family of sample programming languages illustrate this technique.