  The proof of the multi-Regge form of multiple production amplitudes in the
next-to-leading logarithmic approximation is presented for Yang-Mills theories
with fermions and scalars in any representations of the colour group and with
any Yukawa-type interaction. Explicit expressions for the Reggeized gauge boson
trajectory, the Reggeon vertices and the impact factors are given. Fulfilment
of the bootstrap conditions is proved.
