Normal mode instability in the anharmonic lattices has been investigated both analytically and numerically. Double-band structure of instability region in wave vector space of perturbation waves has been found. A critarion for the long- wave modulation instability of running waves wich can be regarded as a generalization of the Lighthill criterion is proposed. The results are disscussed in connection with the problem of coherent structure formation in anharmonic lattices.