Two-fluids interfaces are known to be unstable without surface tension because of the formation of Kelvin-Helmholtz instabilities. In presence of surface tension, local existence results can be proved, but on a time scale that depends a priori dramatically on the surface tension coefficient. We will show that a careful analysis of the formation of Kelvin-Helmholtz instabilities allows us to exhibit a stability criterion generalizing the Rayleigh-Taylor criterion in the one fluid case, and which can be used to explain many physical observations.