Experimental results concerning the supercritical behaviour of instabilities occurring in the thermal convective flow between inclined plates are presented. For inclination δ between 90° and 10° (δ = 0° is the vertical orientation), with the bottom plate hotter, it is known that the primary instabilities are longitudinal convective rolls with axes oriented up the slope. These rolls are found to become wavy at a supercritical Rayleigh number Ra(δ, Pr), with an upslope wavelength which seems to be related directly to the wavelength of the original rolls. Measurements indicate that these transitions take place at Reynolds numbers which are probably too small for the process to be attributed to a shear instability. It is thought that the cross-slope derivative of the buoyancy force, which exists because of the tilted geometry, is important in generating the required vorticity. The transition is crucial to the development of violent unsteadiness. The breaking of the waves leads to turbulence at much lower Rayleigh numbers than those required in convection between horizontal plates. The transition to wavy vortices appears to be very similar to that which occurs for Taylor vortices in cylindrical Couette flow.