Diploid Solanum tuberosum ( tbr), 2n=2x=24, can be crossed with S. verrucosum ( ver) only when the latter is used as a pistillate parent but not reciprocally. This conforms to the phenomenon of unilateral incompatibility (UI) where a self-compatible species, like ver (SC) cannot be used as a male parent to cross with a self-incompatible (SI) parent like tbr. Even if ver x tbr hybrids are made, the F1 hybrids possess cytoplasmic male sterility and thus hinder genetic analysis of crossing barriers. Exceptionally, however, some diploid genotypes of tbr (SI) can be used as pistillate parents to cross with ver, and such exceptional tbr clones are called `acceptors'. Repeated backcrossing of acceptors to ver have resulted in male fertile genotypes that possess tbr cytoplasm and ver nucleus. These genotypes were used for the genetic analysis of `acceptance' and UI in thse experiments. It was found that acceptance of ver-pollen by tbr-pistils is based on a dominant gene A that expresses only in the absence of an inhibitor I. In the F1 hybrids, only the S-allele of tbr was expressed but not that of ver. Concomitant with this observation, it was shown that ver does not produce style-specific S-glycoproteins that are responsible for self-incompatible reaction in diploid potato. Although the the F1 populations were SC, they segregated into SC and SI genotypes giving skewed segregation ratios for this trait. Because of this as well as the disappearance and re-appearance of SC trait in the offspring generations, it was necessary to postulate a more complex interaction between A and I. Models are presented in order to explain acceptance, non-acceptance and the expression of UI. It is concluded that at least four different loci are involved in the expression of UI.