We present a theory of high-order harmonic generation by diatomic molecules exposed to an elliptically polarized laser field. This theory is based on the molecular strong-field approximation with the laser-field-dressed initial bound state and the undressed final state. The interference minima, observed for linear polarization, are blurred with the increase of the laser-field ellipticity. The nth harmonic emission rate has contributions of the components of the T -matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. We analyze the destructive interference condition for this perpendicular component. Taking into account that the aligned molecules are an anisotropic medium for high-harmonic generation, we introduce elliptic dichroism as a measure of this anisotropy and discuss possibilities of its use for determining the molecular structure.
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