Phase matching for optical second-harmonic generation in the helically twisted smectic-C* liquid-crystalline phase is analyzed theoretically. Ten distinctive phase-matched combinations of the fundamental and the second-harmonic eigenmodes exist. The effective second-order nonlinear optical susceptibility and the relation between the optical wave vectors and the wave vector of helical structure are determined for each of the combinations. The results obtained within the standard approximation of the slowly varying amplitude are compared with the exact numerical solutions of the nonlinear wave equation. The discrepancy between the approximative and exact results is crucial only for the two phase-matched combinations that are realized when the second-harmonic frequency is close to the selective reflection band. In this case an additional enhancement of the second-harmonic beam can appear. @S1063-651X~97!05707-3# The phenomenon of optical second-harmonic generation ~SHG! in the ferroelectric smectic-C* ~Sm-C*! phase has recently become very attractive from a fundamental as well as an applicable point of view. Among different SHG characteristics, the possibility for phase matching was investigated most extensively. For this purpose the spontaneously formed Sm-C* helix was unwound by application of a static external electric field @1‐9#. Phase matching in the resulting homogeneous Sm-C* phase was then achieved by a standard technique of compensation of material color dispersion by its birefringence @10#. In addition to the standard phase-matching technique, the helical structure of the Sm-C* phase provides some particular possibilities to achieve an efficient harmonic generation. The optical wave-vector mismatch can be compensated by the wave vector associated with the spatial periodicity of the helix. This is similar to the phenomenon of phase matching in periodically poled materials @11#. In liquid crystals such possibilities were demonstrated and analyzed by Shelton and Shen for optical third-harmonic generation ~THG! in the cholesteric phase @12‐14#. Later, similar features were found by Saha for the electric-field-induced SHG@15#. In this paper we study the phenomenon of optical SHG in the twisted Sm-C* structure. The case of optical beams propagating along the helical axis is examined. The exact numerical solutions of the nonlinear wave equation are related to the analytical solutions within the standard approximation of the slowly varying amplitude. Possible phasematched combinations of optical waves are determined and their relation to the helical periodicity of the structure is analyzed and discussed. The corresponding effective nonlinear susceptibility coefficients are found. The main similarities and differences between SHG in the Sm-C* phase and THG or field-induced SHG in the cholesteric phase are also pointed out. In the discussion we show that our results can explain the prominent increase of the SHG signal, which has been reported by Kajikawa et al. @16# and Furukawa et al. @17# for the situation when the wavelength of the secondharmonic beam coincided with the period of the Sm-C* helix. This particular case has already been analyzed within some approximations in our previous paper @18#.