For a graph $G=(V,E)$, a sequence $S=(v_1, v_2, \cdots, v_k)$ of distinct vertices of $G$ is called \emph{dominating sequence} if $N_G[v_i]\setminus \bigcup_{j=1}^{i-1}N[v_j]\neq\varnothing$ and is called \emph{total dominating sequence} if $N_G(v_i)\setminus \bigcup_{j=1}^{i-1}N(v_j)\neq\varnothing$ for each $2\leq i\leq k$. The maximum length of (total) dominating sequence is denoted by ($\gamma_{gr}^t)\gamma_{gr}(G)$. In this paper we compute (total) dominating sequence numbers for generalized corona products of graphs.