Random amplified polymorphic DNA (RAPD) and simple sequence repeat (SSR) markers were used to construct a partial genetic linkage map in a potato backcross population. The population, derived from two diploid wild Solanum species (frost tolerant, able to cold acclimate S. commersonii; frost sensitive, unable to cold acclimate S. cardiophyllum), was used to map quantitative trait loci (QTL) of non-acclimated relative freezing tolerance (NARFT) and cold acclimation capacity (CAC). Precise assessment of these traits allowed distinction of small but significant differences among 35 backcross genotypes. NARFT and CAC were not correlated in the segregating population, suggesting independent genetic control for these two major components of freezing tolerance. The linkage map spanned 479.4 cM and included 77 RAPD markers and two SSR markers, with 38 RAPD and 10 SSR unassigned markers. Two QTLs for NARFT were detected in two different linkage groups, accounting for 44.0% of the phenotypic variation for this trait. Two QTLs for CAC were detected, accounting for 24.9% of the phenotypic variation for this trait. QTLs for NARFT and CAC were detected at separate genomic regions, in support of the independent genetic control of these two traits. QTLs for NARFT and CAC were detected in a linkage group identified as part of chromosome V, suggesting that such chromosome constitutes a prime candidate for fine-mapping. Due to the relatively small progeny size evaluated in this study, additional QTLs for NARFT and CAC could have been involved but not identified. Therefore, the conclusions derived from this study should be considered preliminary.