The stability of Benard-Marangoni convection is significantly affected by internal heat generation in the fluid layer and by surface tension at the upper free surface. There are two different kinds of instability mode: the thermal mode and the surface tensile mode. At lower values of the Crispation number C, the instability is dominated by the thermal mode. At higher values of C, the system becomes more unstable and creates the surface tensile mode, which is induced by the surface tensile effect. The Crispation number C at the transition between the thermal and the surface tensile modes decreases as the value of internal heat generation increases and that of thermal buoyance decreases.