Uniform cosmological models with deceleration parameter q = constant, are studied in an enlarged relativistic frame-work wherein the universe is regarded as an open thermodynamical system, using Prigogine's hypothesis of creation of matter out of gravitational energy. A broad classification of non-singular models with accelerating and decelerating expansion is given; the big bang (singular) models occur as a particular case corresponding to 'no creation condition' in this regime. The inflationary model with de Sitter expansion belongs to particle creation domain with q = -1. © 1996 OPA (Overseas Publishers Association).