A theoretical and experimental study of amplitude and phase scintillations in line-of-sight links operating at freqeuncies subject to absorption, observed during conditions of atmostpheric turbulence, is presented in this work. The scintillation effects are modeled through temporal spectral density functions and amplitude and phase variances. It is shown that published results on scintillations in atmospheric windows, where the absorption effects can be avoided, are particular cases of the present theory. A heuristic model is also developed, to calculate short term cumulative probability distributions of scintillation intensity, considering the absorption mechanism. Measurement results obtained in two experimental links operating in 55.5 and 36.1 GHz, sharing the same 4.1 Km path over Central London, are use to verify the theory.