The Shapley Concentration is the richest supercluster of clusters in the nearby Universe, and its core is a remarkable complex formed by the ACO clusters A3558, A3562 and A3556, and by the two minor groups SC 1327-312 and SC 1329-314. This structure has been studied in various wavelength bands, revealing that it is probably dynamically very active. In this paper we present 174 new galaxy redshifts in this cluster complex, which are added to the sample of 540 already existing velocities. The spectroscopic observations were performed at the 3.6m ESO telescope at La Silla, equiped with the OPTOPUS multifibre spectrograph, on the nights 1993 February of 21-24.