Hidden algebra is a behavioural algebraic specification formalism for objects. It captures their constructional aspect, concerned with the initialisation and evolution of their states, as well as their observational aspect, concerned with the observable b ehaviour of such states. When attention is restricted to the observational aspect, final/cofree constructions provide suitable denotations for the specification techniques involved. However, when the constructional aspect is integrated with the observatio nal one, the presence of nondeterminism in specifications prevents the existence of final/cofree algebras. It is shown here that final/cofree families of algebras exist in this case, with each algebra in such a family resolving the nondetermi nism in a particular way. Existence of final/cofree families yields a canonical way of constructing algebras of structured specifications from algebras of the component specifications. Finally, a layered approach to specifying complex objects in hidden algebra is presented, with the semantics still involving final/cofree families.