We perform N-body simulations of young triple systems consisting of two low-mass companions orbiting around a significantly more massive primary. We find that, when the orbits of the companions are coplanar and not too widely separated, the chance of a collision between the two companions can be as high as 20 per cent. Collisions between one of the companions (always the less massive) and the primary can also occur in systems with unequal-mass companions. The chance of collisions is a few per cent in systems with more realistic initial conditions, such as with slightly non-coplanar orbits and unequal-mass companions. If the companions start widely separated then collision are very rare except in some cases when the total mass of the companions is large. We suggest that collisions between members of young multiple systems may explain some unusual young multiple systems such as apparently non-coeval companions.