The time-dependent serpentine distortions of the stripe phase of lipid monolayers at the air-water interface are studied by accounting for the effects of line tension and electrostatic forces within the monolayer, as well as viscous forces within both the monolayer and the subphase. It is shown that distortions that have wavelengths of the same order as the stripe widths are expected to grow or decay rapidly, depending on the relation between the stripe width and the equilibrium width. Serpentine distortions with wavelengths much larger than the stripe widths grow or decay much more slowly. Experimental data of Seul and Chen (Phys. Rev. Lett. 1993, 70, 1658-1661) on stripe phases are discussed in terms of these calculations, with the conclusion that the stripes in these phases have equilibrium widths, and that these stripe phases are stable with respect to static serpentine distortions.