Nonlinear evolution of filaments is investigated by taking into consideration of the energy exchange between background and modulational field. It is found that a modulated beam may experience a periodical filamentation. Bespalov Talanov (B T) theory gave the same results of the fastest growing frequency and the cutoff frequency as the nonlinear theory; but a different result of the fastest growth rate. Initially, the modulations grow exponentially, and afterwards, they grow slower than exponential.