This paper presents a study of noniterative implicit finite difference methods for hyperbolic systems. New space-centered methods involving two time levels are considered. An analysis is made of various properties such as solvability, stability, dissipation, dispersion, and efficient solution of the algebraic systems. The computation of shock waves with a CFL number larger than the unity is discussed. Unconditional stability results are proved for a case having several space variables. Accurate solutions of the Euler equations are obtained that offer major reductions in computing costs over explicit methods.