The means of half-sib progenies have been indicated as selection criteria for intra-population improvement while the average of the means of full-sib progenies in diallel analyses have been proposed as predictors, in part, of the means of untested synthetic varieties. When these measures based on progeny means are expressed as deviations from a defined greater population of crosses, they are often termed the general combining ability (GCA). In this study the GCA estimates or a facsimile were theoretically investigated for the one locus, digene, autotetraploid model to verify the genetic basis and its value for selection and prediction in the presence of a naturally occurring phenomena of autopolyploids called gametic disequilibrium with three types of non-additive inheritance. Two breeding objectives were envisioned, the selection of best parents with recurrent selection based on GCA in the continued development of elite populations and the prediction of advanced generation synthetic variety performance. The first generation means of progenies with a potential bias due to gametic disequilibrium were compared to GCA estimation of same progenies in the absence of gametic disequilibrium. The results indicated that testcrossing plants to a population without gametic disequilibrium could be used for selection of best parents. The gametic disequilibrium in the cross may increase or depress selection response dependent on the array of genotypes which happen to be evaluated, on the type of genic action at the locus, and on the frequency of the desirable allele in the testor population. The GCA estimates for prediction of synthetic performance were potentially biased by gametic disequilibrium. An assumption of pollination by the same array of gametes was made for all plants, but obviously was unrealistic for GCA estimation with partial diallels, or with no selfing, and in other situations. The GCA estimate was shown to be an unreliable predictor of synthetic variety performance. When it was assumed that different plants were pollinated by different arrays of gametes, a more realistic situation, no genetic interpretation of GCA values was possible even with purely additive gene action at the locus.