The power-dependent relaxation dynamics of photoexcited charge carriers in a number of LI-VI semiconductor quantum dots have been studied using femtosecond laser spectroscopy. The dynamics are obtained via excitation of the quantum dots with high power 390 nm pulses of 150 fs duration, and probing of the photoexcited species by monitoring the change in absorption at 790 nn as a function of time. Particles with vastly differing surfaces, sizes, electronic structures, and solvents all show a fast 1.5-4 picosecond decay component which grows in with power, a 17 ps (CdSe) or 50 ps (CdS and Cd0.5Zn0.5S) decay component, and some transient absorption persisting beyond 600 ps. The power-dependent component for CdSe quantum dots in glass has a 1.5 ps decay time constant, while for the liquid dispersed CdS and Cd0.5Zn0.5S quantum dots it has 2-4 ps decay time constants. This variation in the time constant is due to its power dependence, the time constant decreases with increasing power. It is also shown that the power-dependent decay is only weakly dependent on surface, size, and electronic structure. With the assistance of a power-dependent nanosecond fluorescence study, we have assigned the power-dependent decay primarily to exciton-exciton annihilation. This decay mechanism becomes dominant under high intensity excitation where multiple photoexcited charge carriers are created in each quantum dot, leading to trap state saturation and an accumulation of band edge excitons. Auger recombination may also play an important role at very high excitation intensities.