In some aspects, systems for forming hydrogels are provided that comprises (i) a reactive multi-arm polymer that comprises three or more polymer arms linked to a core region, at least three of the polymer arms comprising a reactive moiety comprising a cyclic-imidyl-oxycarbonyl- end group and (ii) a polyamino compound comprising at least two amino (NH.sub.2) groups, wherein the reactive multi-arm polymer and the polyamino compound react to form crosslinked hydrogels that do not contain ester groups and have long-term stability in vivo. In other aspects, the present disclosure pertains to crosslinked hydrogels formed from such systems and methods of treatment using such systems.