In this paper, a new class of multifunctions, called generalized alpha (mu_{X};mu_{ Y} )-continuous multifunctions, has been dened and studied. Some characterizations and severalproperties concerning generalized alpha (mu_{X};mu_{ Y} )-continuous multifunctions are obtained. The re-lationships between generalized alpha (mu_{X};mu_{ Y} )-continuous multifunctions and some known con-cepts are also discussed.