The coalescence collision of two liquid drops is studied using a Galerkin finite element method in conjunction with the spine-flux method for the free surface tracking. The effects of Reynolds number, impact velocity, drop size ratio, and internal circulation on the coalescence process is investigated. The long time oscillations of the coalesced drop are also studied and curves for the variations of the period and decay factor are provided as a function of the number of oscillations. In the study of non-equal-size drop collision, traces of different fluid particles are calculated to illustrate the liquid mixing during the collision.