Reduced models for control problems of large size is one of the fundamental issues in systems and control theory. Among various techniques, methods of truncation are the states that allow a more accurate representation of the system reduced. Many of these methods need to solve one or more Lyapunov equations (usually coupled), sometimes requiring the Cholesky factor of the solution. In this thesis pesentan algorithms for sequential and parallel blocks for solving these equations. Are designed algoritomos fine, medium and combined, based on the method of Hammarling, for shared memory multiprocessors. Have also developed parallel algorithms for multicomputadores pass messages using, adapting and developing the algorithms against the nda and cyclical used in solving triangular linear systems, we also present new algorithms based on the method of the matrix sign function for full resolution of the Lyapunov equations for continuous time fitting into the standard case and generalized by calculating both the explicit solution of the Cholesky factor, all the algorithms have been implemented in several parallel computers have been evaluated and the results.