Let $R$ be a semiprime ring and $\alpha$ be an automorphism of $R.$ A mapping $F:R\to R$ (not necessarily additive) is called multiplicative generalized $(\alpha,\alpha)$-derivation if there exists a unique $(\alpha,\alpha)$-derivation $d$ of $R$ such that $F(xy)=F(x)\alpha(y)+\alpha(x)d(y)$ for all $x,y\in R.$ In the present paper, we intend to study several algebraic identities involving multiplicative generalized $(\alpha,\alpha)$-derivations on appropriate subsets of semiprime rings and collect the information about the commutative structure of these rings.