  The evolution of young compact star clusters is studied using N-body
simulations in which both stellar evolution and physical collisions between
stars are taken into account. The initial conditions are chosen to represent
R136, a compact star cluster in the 30 Doradus region of the Large Magellanic
Cloud. The present runs do not include the effects of primordial binaries. We
find that physical collisions between stars in these models are frequent, and
that the evolution of the most massive stars and the dynamical evolution of the
cluster are closely coupled. In all cases, a single star grows steadily in mass
through mergers with other stars, forming a very massive (>100 Msun) star in
less than 3-4 Myr. The growth rate of this runaway merger is much larger than
estimates based on simple cross-section arguments, mainly because the star is
typically found in the core and tends to form binaries with other massive stars
there. The runaway is ``rejuvenated'' by each new collision, and its lifetime
is extended considerably as a consequence. Observationally, such a star will
appear in the Hertzsprung-Russell diagram as a blue straggler. When the runaway
forms a black hole, the binary in which it is found is usually dissociated.
