collision the momentum transfer may arise due to interaction of the emitting particle with the opposite beam as a whole (due to coherent interaction with averaged field of the beam) and due to interaction with an individual particle of the opposite beam. Here we are considering [*the incoherent*]{} process only (connected with the incoherent fluctuation of density) and so we have to subtract the coherent contribution. The expression for the bremsstrahlung spectrum found in [@BKS1] contains the mean value $<{\bf q}^2>$, while the coherent contribution contains $<{\bf q}>^2$ and this term has to be subtracted. We encountered with an analogous problem in analysis of incoherent processes in the oriented crystals [@BKS2] where it was pointed out (see p.407) that the subtraction has to be done in the spectrum calculated in [@BKS1]. Without the subtraction the results for the incoherent processes in oriented crystals would be qualitatively erroneous.

In Sec.2 a qualitative analysis of the incoherent radiation process is given. In Sec.3 the general formulas for the spectral-angular distributions of incoherent bremsstrahlung are derived. The incoherent bremsstrahlung spectrum for the Gaussian beams is calculated in Sec.4 in the form of double integrals. In specific case of narrow beams (the size of 