The in vitro biological activities of novel derivatives of methyl and ethyl 2-(4-oxo-8-aryl-2H-3,4,6,7-tetrahydroimidazo[2,1-c][1,2,4]triazin-3-yl)acetates (3a, 3d-j) have been evaluated and are reported. The final heterobicycles (3a-j) were obtained from monocyclic 1-aryl-2-hydrazonoimidazolidines (2a-f) by addition and cyclization reaction with fumaric acid esters. In particular, compounds 3d and 3e were found to exhibit comparable antibacterial potencies in vitro as that of ampicillin. Heterobicycles of the 3e, 3g and 3j type were screened for their antiviral activities against the selected viruses' DNA (human adenovirus type 5-Ad-5) and RNA (human enterovirus-Echo-9). Simultaneously, their cytotoxicities towards HEK-293 and GMK cells were established. In particular, heterobicycle 3j, completely non-toxic for GMK cells, was found to exhibit virucidal properties against Echo-9 virus justifying its further investigation as the potential antiviral agent.