Coupled buoyancy (Benard) and thermocapillary (Marangoni) convection i
n a thin fluid layer of a viscoelastic fluid are studied. The viscoela
stic fluid is modeled by Jeffreys' constitutive equation. The lower su
rface of the layer is in contact with a rigid heat-conducting plate wh
ile its upper surface is subject to a temperature-dependent surface te
nsion. The critical temperature difference between both boundaries cor
responding to the onset of convection is calculated. The role of the v
arious viscometric coefficients is discussed. In the appendix it is sh
own that Jeffreys' constitutive relation is easily derived from thermo
dynamic considerations based on extended irreversible thermodynamics.