We report on near-infrared and optical observations of the GRB 970616 error box and of the X-ray sources discovered by ASCA and ROSAT in the region. No optical transient was found either within the IPN band or in the X-ray error boxes, similarly to other bursts, and we suggest that either considerable intrinsic absorption was present (like GRB 970828) or that the optical transient displayed a very fast decline (like GRB 980326 and GRB 980519). Based on observations collected at the German-Spanish Astronomical Centre, Calar Alto, operated by the Max-Planck-Institut für Astronomie, Heidelberg, jointly with the Spanish National Commission for Astronomy.Based on observations carried out at the Danish 1.54-m Telescope on the European Southern Observatory, La Silla, Chile.