The dinuclear complexes [Co2(CO)6{P(OAr)3}2] (1a, Ar = Ph; 1b, Ar = o-Tol) were prepared and reacted with PhC≡CH and PhC≡CPh to yield dimetallatetrahedranes [{(ArO)3P}(OC)2Co-Co(μ-RC≡CPh)(CO)2{P(OAr)3}] (3a, Ar = Ph, R = H; 3b, Ar = o-Tol, R = H; 3c, Ar = Ph, R = Ph; 3d, Ar = o-Tol, R = Ph). The main reaction of diphenylacetylene was accompanied by a side reaction, leading to the dissociation of a P(OAr)3 ligand for the formation of mono(phosphite) complexes [{(ArO)3P}(OC)2Co-Co(μ-PhC≡CPh)(CO)3] (2b, R = Ph; 2d, R = o-Tol). The crystal structures of 1b, 3a, and 3d were determined along with that of the mono(phosphite) complex [{(PhO)3P}(OC)2Co-Co(μ-PhC≡CPh)(CO)3] 2b.