A theory of high-order harmonic generation by arbitrary polyatomic molecules is introduced. A polyatomic molecule is modeled by an (N + 1)-particle system, which consists of N heavy atomic (ionic) centers and an electron. After the separation of the center-of-mass coordinate, the dynamics of this system is reduced to the relative electronic and nuclear coordinates. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are introduced. For neutral polyatomic molecules the derived expression for the T-matrix element takes a simple form. The interference minima in the harmonic spectrum are explained as a multiple-slit type of interference. This is illustrated by numerical examples for the ozone (O-3) and carbon dioxide (CO2) molecules.
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