We study the occurrence of physical collisions between stars in young and compact star cluster .
The calculations are performed on the GRAPE-4 with the starlab software environment which include the dynamical evolution and the nuclear evolution of all stars and binaries .
The selection of the initial conditions is based on existing and well observed star clusters , such as R136 in the 30 Doradus region in the Large Magellanic Cloud and the Arches and Quintuplet star clusters in the vicinity of the Galactic center .
Collisions between stars occurred rather frequently in our models .
At any time a single star dominates the collision history of the system .
The collision rate of this runaway merger scales with the initial relaxation time of the cluster and is independent on other cluster parameters , such as the initial mass function or the initial density profile of the cluster .
Subsequent encounters result in a steady grow in mass of the coagulating star , until it escapes or explodes in a supernova .
The collision rate in these models is about 2.2 \times 10 ^ { -4 } collisions per star per Myr for a cluster with an initial relaxation time of 1 Myr .