The onset of the wave resistance, via generation of capillary-gravity waves of a small object moving with velocity V, is investigated experimentally. Because of the existence of a minimum phase velocity V(c) for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases waves or rotons are produced at V>V(c) due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to sqrt[V-V(c)] for various fluids.