In order to address the mechanism of rich cluster formation I present recent analyses on formation of the young rich clusters in the LMC and the Antennae galaxies. In the LMC R136 is the most outstanding cluster which harbors 400 O/B stars in itssurroundings. A new analysis of the HI data taken with the ATCA shows that two velocity components whose velocity separation is ~50 km/s collided with each other 2 Myrs ago and the collision triggered the formation of the cluster and the O/B stars.The scenario is supported by the simulations by Bekki and Chiba 2007, which show that the LMC and SMC encountered closely 0.2 Gyrs ago and that the tidal force removed the HI gas from both the LMC and the SMC. The HI gas is now falling back onto the LMC disk to trigger the star formation. The Antennae galaxies at a larger distance allow us to make a similar analysis on CO data taken with ALMA. We found similar possible collision signatures toward a few of the young cluster candidates in the overlapping area, where two CO clouds of ~100 km/s velocity separation are interacting dynamically. Triggers of cluster formation are a probable outcome of the collisions. I will present a few more cases in the Local Group which lend support for the galactic collisional events as triggers of rich cluster formation.