We　study　two　unrelated　machine　scheduling　problems　with　machine　dependent　release　dates　to　minimize　the　makespan.　For　the　case　with　fixed　processing　time　where　processing　job　j　on　machine　i　requires　time　P-ij　and　incurs　a　cost　of　c(ij),　we　derive　a　2-approximation　algorithm.　For　the　problem　with　variable　processing　times　where　the　cost　increases　linearly　as　the　processing　time　decreases,　we　propose　a　(2+epsilon)-approximation　algorithm.