The class of <$Egamma>-generating matrices and its subclasses of regular and singular <$Egamma>-generating matrices were introduced by D. Z. Arov in [8], where it was shown that every <$Egamma>-generating matrix admits an essentially unique regular-singular factorization. The class of generalized <$Egamma>-generating matrices was introduced in [14, 20]. In the present paper subclasses of singular and regular generalized <$Egamma>-generating matrices are introduced and studied. As the main result of the paper a theorem of existence of regular-singular factorization for rational generalized <$Egamma>-generating matrix is found.

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