In this paper. linear overstable convection of a viscoelastic fluid layer with upper deformable free surface is investigated. For the sake of comparison, the corresponding case for nondeformable free surface is also investigated. The Oldroyd＇s viscoelastic model constitutive equation with relaxation and retardation times is made use of. Calculations are made with the Maxwell＇s model as a particular case. It is supposed that the lower flat surface is at fixed temperature and that the upper deformable free surface is at fixed heat flux. Two cases are investigated which differ due to the mechanical boundary conditions imposed on the lower flat wall, that is, it may be solid or stress free. It is found, for different values of the Galileo number, that for relaxation times that are large enough the curves of the critical Rayleigh numbers are lower than those of stationary convection and those of overstability of the Newtonian fluid with deformable free surface. When the lower surface is rigid maxima in the curves of criticality against the relaxation time are found. When the lower surface is stress free, jumps and maxima are found in the curves of the critical wavenumber and frequency against the relaxation time. To explain these jumps and maxima. based on results previously reported in the literature, it is shown that gravity acts as an extra body force through the surface deformation, playing a dual role on the stability of the convective viscoelastic fluid layer.