We consider the nonlinear electrohydrodynamic stability of wave packet
s of capillary-gravity waves in fluids of any depth; they travel predo
minantly in one direction, however the wave amplitudes are modulated s
lowly in both horizontal directions. The method of multiple time scale
s is used to obtain a nonlinear Schrodinger equation describing the be
haviour of the perturbed system. The envelope solutions of steady form
are obtained in terms of the Jacobian elliptic functions. It follows
that various types of envelope solutions of the modulated Stokes waves
may exist depending on the relative signs of terms representing dispe
rsive and nonlinear effects; the solitary and periodic envelope soluti
ons for the general case of any liquid depth are described. It is also
shown that the evolution of the envelope is governed by two coupled p
artial differential equations with cubic nonlinearity. The stability o
f solitons with respect to transverse perturbations is investigated It
is found that such wave packets are stable to short waves, and unstab
le to long disturbances, and the envelope solitons and the waveguides
are always unstable, and the stability of the system depends on the va
lues of the dielectric constant ratio, the electric held the wavenumbe
r, and the depth of the fluid.