The influence of rotational and vibrational energy relaxation on the stability of laminar boundary layers in supersonic flows is investigated. The relaxation models are derived from both statistical thermodynamics and from published experimental data in the field of physical chemistry. Rotational relaxation dampens high-frequency instabilities, consistent with the well known damping effect of rotational relaxation on acoustical waves. Conversely, vibrational relaxation has a destabilizing effect in wind-tunnel flows, with the effect increasing in strength with increasing stagnation temperature. This destabilizing effect is also found for blunt bodies in free-fight, although the effect is weaker than that in wind-tunnels.