  Numerical arguments are presented for the existence of regular and black hole
solutions of the Einstein-Skyrme equations with a positive cosmological
constant. These classical configurations approach asymptotically the de Sitter
spacetime. The main properties of the solutions and the differences with
respect to the asymptotically flat ones are discussed. It particular our
results suggest that, for a positive cosmological constant, the mass evaluated
as timelike infinity in infinite. Special emphasis is set to De Sitter black
holes Skyrmions which display two horizons.
