A topological space X is called k-space if X is a Hausdorff space and X is an image of a locally compact space under a quotient mapping. A natural question arises: when a k-space satisfies that its product with every k-spaces is also a k-space? Michael showed that a k-space has this property iff it is a locally compact space. A similar question, related to the class of quasi-k- spaces, Hausdorff images of locally countably compact spaces under quotient mappings, was answered by M. Sanchis. The study of k-spaces and quasi-k-spaces suggests to define, in a natural way, the class of sequentially-k-spaces, namely, the class of Hausdorff images of locally sequentially compact spaces under quotient mappings. In this paper the class of sequentially-k-spaces is introduced and investigated.