The excitation of absolute instabilities in three-wave parametric couplin g processes in inhomogeneous plasmas has been studied analytically . A detailed examination of the full fourth-order set of differential equations describing such processes in infinite media confirms the WKB-criterion that absolute instabilities arise only if . A model calculation using the WKB-approximation has also been carried out to study the effects of finite plasma extent and pump depletion; conditions for the excitation of absolute instabilities in this case have also been obtained.