In this paper, a new class of multifunctions, called generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions, has been defined and studied. Some characterizations and severalproperties concerning generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions are obtained. The relationships between generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions and some known concepts are also discussed. Manuscript profile