The speed of sound v is calculated for asymmetric nuclear matter within the general framework of a finite temperature Green's function method with normal pair cutoff approximation and Skyrme interactions. A rather strong dependence of v on ..cap alpha.., the asymmetry coefficient, is observed at high density. Causal violation of v at high density and/or high temperature is studied. This violation may be avoided if the Skyrme interaction parameters at high density may be readjusted to obey the conditions -1