Off-shell gluon production in interaction of a projectile with 2 or 3 targets

Within the effective QCD action for the Regge kinematics amplitudes for virtual gluon emission are studied in collision of a projectile with two and three targets. It is demonstrated that all un- Feynman singularities cancel between induced vertices and rescattering contributions. Formulas simplify considerably in a special gauge which is a straightforward generalization of the light-cone gauge for emission of real gluons.