For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce ($alpha$, $delta$)-skew Armendariz rings which are a generalization of $alpha$-rigid rings and Armendariz rings, and investigate their properties. A semi prime left Goldie ring is $alpha$-weak Armendariz if and only if it is $alpha$-rigid. Moreover, we study on the relationship between the Baerness and p.p. property of a ring R and these of the skew polynomial ring R[x; $alpha$, $delta$] in case R is ($alpha$, $delta$)-skew Armendariz. As a consequence we obtain a generalization of [11], [14] and [16].