In this paper we present a set of numerical simulations designed to study the interaction process of HII molecular clouds. For the initial conditions we assume head-on and oblique collisions of binary identical clouds placedadjacent to one another, with their surfaces just in contact. The colliding initial clouds are uniform density molecular gas spheres with rigid body rotation. The cloud initial conditions are chosen to favor its gravitational collapse as an isolated system. To study the effect of the self-gravity of the cloud in the collision process, we consider several models in which the approaching speed of the colliding clouds increases from zero up to several times the initial sound speed of the barotropic gas. We present the outcome of these collision models for several values of the impact parameter b, which depends on the initial radius of the cloud. We have explored the parameter space of the approaching velocity Vapp of the colliding clouds for configurations that may result in seeds for the formation of more complex systems. Such systems are expected to include filaments and gas clumps, where the star formation process is still possible despite the occurrence of the collision. We show hereby that collisions may have a major and favorable influence on the star formation process.