  In this paper, we investigate the impact of the phase conversion speed on the
properties of hybrid stars with sequential sharp QCD phase transitions. We
consider that these hybrid stars possess an inner (outer) core of CFL (2SC)
quark matter surrounded by hadronic matter. Assuming that the phase conversions
can be slow or rapid, we analyze the dynamical stability of these objects. In
particular, we present our predictions for the mass-radius profile and the
fundamental eigenfrequencies of hybrid stars with sequential QCD first order
phase transitions. Our results demonstrate that the usual stability criteria
i.e. $\partial M/ \partial P_0 \geq 0$, is sufficient only if both conversions
are rapid. Moreover, we show that if any of the interfaces has a slow
conversion speed, the fundamental eigenfrequencies are significantly modified.
