In this paper, we construct four$M$-ary sequence families from apower residue sequenceof odd prime period$p$and its constant multiple sequences using the shift-and-add method, when$M$is a divisor of$p-1$. We show that the maximum correlation values of the proposed sequence families are upper-bounded by$2\sqrt {p} +5$or$3\sqrt {p} +4$. In addition, we prove that the linear complexity of each sequence in the proposed families is either$p\!-\!1$or$p\!-\!{p-1 \over M}\!-\!1$. We also construct an$M$-ary sequence family fromSidel'nikov sequencesof period$p^m-1$by applying the same method, when$M$is a divisor of$p^m-1$. The proposed sequence family$\mathtilde {\cal F}_{\mmb s}$has larger size than the known$M$-ary Sidel'nikov sequence families, whereas they all have the same upper bound on the maximum correlation.