[en] The modular invariant partition function of the two-dimentional Ashkin-Teller model on a line of continuously varying criticality is obtained. The second magnetic exponent is predicted to be 9/8. Derivation of the partition function in terms of gaussian field theories is also presented. Using chiral gaussian fields we construct the partition function for free boundary conditions, in terms of which the numerically observed spectrum is reproduced and, in particular, the appearance of N=2 supersymmetry at three particular points on the critical line is demonstrated. We discuss the fermion operator content by constructing the partition function for antiperiodic boundary conditions. (orig.)