Most of the work on exact models representing gravitational waves in general relativity has been concerned with spacetimes which are,at least in some directions, asymptotically flat. Here we treat gravitational waves in one of the simplest but everywhere curved cosmological model. We give the physical interpretation of exact "type - N solutions" of Einstein´s equations with cosmological constant presented recently by García Días and Plebanski. We show that some of these solutions may be interpreted as gravitational waves propagating in the de Sitter universe. (According to present consensus, this unvierse represents the inflationary stage of our Universe.) The analysis also reveals that tha solutions can serve as the illustration of the cosmological no-hair theorem: they approach the de Sitter space-time asymptotically in time.