The concept of a transfer function is extended to general dynamic systems described by non-regular linear algebraic and integro-differential equations. The input consistency and uniqueness of the system output for the given consistent input are discussed. These two properties are closely related to the existence of a transfer function which itself does not need to be unique. Input-output equivalence in the sense that two systems have the same output for the given consistent input is proved to be necessary and sufficient for the existence of an input-output isomorphic map between the solution spaces of the systems under zero initial conditions.