In the present paper we have investigated the excitation of a plasma wave of frequency &Dgr;&ohgr;=&ohgr;1∼&ohgr;2in a collisionless hot plasma by two coaxial Gaussian EM beams of frequencies &ohgr;1and &ohgr;2and propagating in the same direction. The mechanism of nonlinearity is assumed to be ponderomotive force arising because of Gaussian intensity distribution of the beams. In the presence of two beams, the nonlinearities introduced by two beams are additive if the difference frequency &Dgr;&ohgr; is comparable to &ohgr;1or &ohgr;2and, hence, cross focusing occurs. For a given power of one beam, the nature of self‐focusing becomes considerably modified by changing the power of the second beam. The power associated with the excited plasma wave, which depends on the background electron concentration and the intensity of the two beams, becomes drastically modified with the distance of propagation. The theory presented here is also applicable to a slightly inhomogeneous collisionless hot plasma within the WKB approximation.