This paper discusses a new specification method for algebraic data types consisting of an algebraic analogon to domain equations as known from Scott’s theory (1971) of order-theoretic data types. The main result is that strongly persistent algebraic domain equations always have an initial solution, and there is a simple syntactic method to construct a specification of this initial solution. Examples illustrate the usefulness of implicit specifications in certain cases. Then, a parametric version of algebraic domain equations is introduced having parameterized data types as solutions. It is shown that there is always a solution that can be obtained syntactically as in the nonpnrameterized case. This solution behaves consistently with respect to parameter passing.