Results of experiments are presented on the behavior of turbulent flames in mixtures of methane, ethane, and propane with air. Tests were performed in two explosion tubes, one with an inner-diameter of 174 mm and the other of 520 mm. It was found that (similar to hydrogen combustibles) the flame acceleration can be weak or strong resulting either in slow subsonic flames, or in fast supersonic combustion regimes. Critical mixture compositions for the threshold between slow and fast combustion regimes were determined in the tests. In lean mixtures of hydrocarbon fuels, the critical compositions were not dependent on the tube size. On the rich side, a significant scale effect was observed. Effect of the basic flame properties, such as mixture expansion ratio, laminar flame thickness, and effective, activation energy on the critical conditions for strong flame acceleration is discussed.