Let M be a matching in graph G. A vertex covered by M is said to be strong vertex for M, if it has degree one in the graph induced in G by the vertex set covered by M. A strong matching M is a matching in which every vertex covered be M is strong for M. A semistrong matching M is defined by requiring that each edge of M has at least one strong vertex for M. The minimal number of classes needed to partition E(G) into matchings, strong matchings, and semistrong matchings are called chromatic index (Â0(G)), the strong chromatic index (Â0 S(G)), and the semistrong chromatic index (Â0 SS(G)), respectively. Semistrong edge coloring of a graph has been introduced by Andre´as Gy´arf´as and Alis Hubenko [1]. In this work we show two tight lower bounds for semistrong chromatic indices of graphs, and various tight upper bounds for semistrong chromatic indices of some products of graphs. In particular, we prove the following theorems (and a few others very similar to the ones about strong edge coloring shown by Oliver Togni [2]).formula