Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over LLTS, including usual process-algebraic operators, logic connectives (conjunction and disjunction) and standard temporal modalities (always and unless), have been given. However, no attempt has been made so far to develop the general theory concerning (nested) recursive operations over LLTS and a few fundamental problems are still open. This paper intends to study this issue in a pure process-algebraic style. A few fundamental properties, including precongruence and the uniqueness of consistent solutions of equations, will be established.