  Recently energy exchange between two filaments crossing at small angle and
with power slightly above the critical for self-focusing $P_{cr}$ was
experimentally demonstrated. In this paper we present a model describing the
process of this transfer through degenerate four-photon parametric mixing. Our
model confirms the experimental results that the direction of energy exchange
depends on the relative transverse velocity (incident angle), laser intensity
and initial distance between the pulses (relative initial phase). We also
investigate the interaction between two collinear filaments in order to explain
the filaments number reduction for powers close to $P_{cr}$ in multi-filamental
propagation.
