The Euler equations describe inviscid compressible fluid flow and form a system of four nonlinear partial differential equations. We discuss the implementation of a multigrid solver for the two-dimensional Euler equations on a distributed memory multiprocessor. The discretization in space is based on quadrilateral cells, forming a "logically rectangular" grid. The parallelism is introduced by a decomposition of the domain into subdomains. Several relaxation schemes are considered. Some of these relaxation schemes are also used as smoother in the multigrid implementation. Timings and efficiency results obtained on the Intel iPSC/2 hypercube are discussed.