A single-server processor-sharing system with M job classes is analyzed in the steady state.The scheduling strategy considered divides the total processor capacity in unequal fractions among the different job classes.More precisely, if there are N~jobs of classj in the system, j = 1, 2 ..... M, each class k job receives a fraction gh/(~M.~giN~) of the processor capacity.Earlier analyses of this system are shown to be incorrect and new expressions for the conditional expected response times Wk(t) of class k jobs with required service time t are obtained (for general required service time distributions).These yield the asymptotic behavior of W~(t) as t ~ oo and rather simple formulas in the exponential case.The unconditional average response times are also obtained.