Stoichiometric acetylene-oxygen mixtures diluted by argon are widely used in normal detonation waves but have not yet been used in oblique detonation waves (ODWs). The present study simulates ODWs in acetylene-oxygen-argon mixtures, with a dilution ratio Phi = 50%-90%, using the reactive Euler equations with a detailed chemistry model, and describes the characteristics of acetylene ODWs. Similar to ODWs in hydrogen-air mixtures, the transition from the oblique shock wave to ODW may be either abrupt or smooth and the effects of Phi are investigated with a variable incident Mach number M-0. When M-0 changes between 8 and 10, the transition is abrupt in the case of Phi = 50%, while it is smooth in the case of Phi = 90%. In the case of Phi = 70%, a high M-0 corresponds to a smooth transition, while a low M-0 corresponds to an abrupt transition. A further study on the initiation mechanism was performed by comparing the numerical initiation length with the length obtained via the constant-volume combustion calculation, which demonstrated that the initiation is kinetic-controlled in the cases of Phi = 70% and 90%, but wave-controlled in the case of Phi = 50% with M-0 below 8.5. Moreover, an initiation structure featured by two-shock in the product was observed for the first time, and its formation mechanism is qualitatively discussed and compared to hydrogen ODWs. Published under license by AIP Publishing.