This paper develops an approach for restoration of data from comprehensive two-dimensional gas chromatography (GCxGC), a powerful new technology for chemical separations. GCxGC restoration is required to separate coeluting (i.e., overlapping) peaks. The GCxGC process is modeled as a two-dimensional linear, shift-variant system, based on the properties of chemical compounds and gas chromatography. The model can account for nonhomogeneous peak shapes and separability of the two instrument columns. The restoration problem is formulated to minimize the difference between observed GCxGC data and an ideal separation, subject to the physically meaningful constraints: nonnegativity, volume preservation, and unimodality. The paper develops a constrained alternating least-squares (CALS) method for solving the restoration problem. Experimental results based on simulation and real GCxGC data indicate that the proposed model and CALS method perform well for GCxGC restoration.