A detailed study of cosmological models with constant deceleration parameter q is undertaken in the framework of Brans-Dicke theory. These models are divided into two categories: (i) singular models with expansion driven by big-bang impulse, (ii) non-singlar models with expansion driven by creation of matter particles. Prigogine's hypothesis of creation of matter out of gravitational energy is analysed and extended to BD cosmology. To accommodate the creation of new particles, the universe is regarded as an open thermodynamical system and the energy conservation equation is modified with the incorporation of a creation pressure term pc in the energy-momentum tensor {Mathematical expression}. The exact solutions of the field equations of BD theory with {Mathematical expression} are obtained using the power law relation Φ=KRα, which leads to models with constant q. The behaviour of the solutions is investigated for different range of values of a. The role played by the BD scalar field Φ and creation of matter particles in the expansion of the universe is investigated. It is found that one particular model with constant q has exponential expansion. © 1994 Plenum Publishing Corporation.