In this paper we present a new natural deduction calculus for structured algebraic specifications and study proof transformations including cut elimination. As underlying language we choose an ASL-like kernel language which includes operators for composing specifications, renaming the signature and exporting a subsignature of a specification. To get a natural deduction calculus for structured specifications we combine a natural deduction calculus for first-order predicate logic with the proof rules for structured specifications. The main results are soundness and completeness of the calculus and convergence of the associated system of proof term reductions which extends a typed l-calculus by appropriate structural reductions.