Massive contact binaries contain two early-type stars that have filled their respective critical Roche lobes and share a common envelope. Their formation and evolution are still unknown. Searching for massive binaries in special evolutionary stages is required to solve this problem. Many massive binaries in the Andromeda galaxy (M31) have been found out and they provide an ideal laboratory to explore the formation of massive contact binaries and to test evolutionary models in massive binaries. By analyzing the light curves of two massive binaries containing twin components, M31V J00452011+4145037 (hereafter J004520) and M31V J00450522+4138462 (hereafter J004505), observed by Vilardell et al., we found that J004520 is a semidetached binary with a mass ratio of 0.924 and a lobe-filling secondary, while J004505 is a deep-contact binary with a mass ratio of 0.974 and a fill-out factor of 88%. Both of them evolved from originally detached binaries via case A mass transfer and are at a critical evolutionary state with the shortest possible period and the highest possible mass ratio (q = 1). The evolution of J004520 has passed the critical state and cannot evolve into a contact binary, while J004505 is just close to the key state. The asymmetric light curve of J004505 is explained by the presence of a hot spot on the less-massive component caused by mass transfer from the more-massive one; the same conclusion can be obtained from the O - C curve. These results support the conclusion that massive contact binaries are formed from mass transfer between the two components and only some systems can evolve into the contact stage.