The [6π + 2π]-cycloaddition of alkynes to 1-methyl-, propyl-, benzyl-, and hydroxymethyl-substituted 1,3,5-cycloheptatrienes in the presence of catalytic systems Ti(acac)2Cl2-Et2AlCl and Co(acac)2(dppe)/Zn/ZnI2 was performed for the first time to give practically valuable bicyclo[4.2.1]nona-2,4,7-trienes in high yields (72-88%). The structures of the obtained bicyclic compounds were reliably proved by NMR methods and X-ray diffraction analysis. The newly synthesized bicycles have been investigated for their in vitro cytotoxic activity against Jurkat, K562, U937, and HL60 tumor and normal cell lines and induction of apoptosis.