Response is made to Y. I. Salamin's preceding Comment [Phys. Rev. ST Accel. Beams 3, 059001 (2000)]. We confirm the areas of applicability of the original and Salamin's general solutions and discuss new applications of the developed formalism.PACS numbers: 13.60. Fz, 14.60.Cd, 03.65.Ge, 41.20.Jb In his Comment, Salamin [1] proposes a generalized format for the exact solution of the equations of motion of relativistic electrons in the field of two plane electromagnetic waves attained by Amatuni and Pogorelsky [2]. The revised form of the solution, otherwise equivalent to one derived in [2], facilitates an explicit treatment of the problem of two copropagating electromagnetic waves that are different in frequency. As soon as the equivalency of the revised solution [given by Eqs. (4), (14)- (16) since the initial purpose of their study was to uncover the phase sensitive effects (x-ray radiation and the electron energy modulation) occurring when the relativistic electron passes a standing electromagnetic wave.A practical motivation for the Amatuni and Pogorelsky study [2] was to develop a novel tool to diagnose electron microbunches grouped to laser wavelength. Such microbunching is essential for attaining a monoenergetic regime of direct electron acceleration in laser field. Microbunches grouped to the 10 mm period have been produced via an inverse free-electron laser process and demonstrated by the coherent transition radiation method at the BNL accelerator test facility (ATF) [3]. The first attempt to phase such "dotted" electron beams into the inverse Cherenkov laser accelerator module is under way at the ATF [4,5].As stated in the preceding paragraph, the goal of developing a novel method of microbunch diagnostics was accomplished by deriving phase sensitive expressions for intensity of the nonlinear component of electron Thomson scattering and for electron energy modulation [2].Needless to say, the solution of the general equations of the electron motion in interfering waves, in addition to the standing wave case, allows excursions to other two-wave combinations. Among them is the problem considered in [1] of a relativistic electron exposed to copropagating waves of different frequency that is applicable to the so-called vacuum beat wave accelerator (VBWA) [6].Not undermining the validity of the solutions attained in [1] and [2], the author wishes to use this occasion to comment on the applicability of the developed formalism to real world situations.Both of the referenced papers address the solution of the electron motion in interfering plane waves. Furthermore, in order to obtain the net acceleration effect in copropagating waves or phasing effects in counterpropagating waves (standing wave) the electron-laser interaction length shall be terminated by some sort of screen or cavity mirror. Both assumptions (plane waves and cavities) look impractical when the laser field is appreciably strong to induce relativistic quiver electron motion. Indeed, ultrahigh electromagnetic field, attractive for novel metho...