Algorithm 961: Fortran 77 subroutines for the solution of skew-Hamiltonian/Hamiltonian eigenproblems. Skew-Hamiltonian/Hamiltonian matrix pencils λ S — H appear in many applications, including linear-quadratic optimal control problems, H∞-optimization, certain multibody systems, and many other areas in applied mathematics, physics, and chemistry. In these applications it is necessary to compute certain eigenvalues and/or corresponding deflating subspaces of these matrix pencils. Recently developed methods exploit and preserve the skew-Hamiltonian/Hamiltonian structure and hence increase the reliability, accuracy, and performance of the computations. In this article, we describe the corresponding algorithms which have been implemented in the style of subroutines of the Subroutine Library in Control Theory (SLICOT). Furthermore, we address some of their applications. We describe variants for real and complex problems, as well as implementation details and perform numerical tests using real-world examples to demonstrate the superiority of the new algorithms compared to standard methods.