To understand the genetic control of grain filling duration (GFD), i.e., the number of days from anthesis to physiological maturity, we studied the $F_1,;F_2,;BC_1; and;BC_2$ generations of six spring wheat crosses from nine varieties/genotypes. Generation mean analysis for gene effects indicated that one or more types of epistasis were significant in all crosses. In each pairing, the $F_1;and; F_2$ means were either intermediate or closer to the mean of the parent having the longer GFD. Our narrow-sense heritability estimate was reasonably high, at 47.67 (based on diallel analysis). This demonstrated that progress could be made from the selection in these crosses for either long or short GFD. The two early varieties that had identical maturity durations differed in their GFD values, indicating that maturity dates are not good criteria when choosing parents for modifying GFD. To utilize favorable additive x additive effects during this selection, we suggest that a single seed descent (SSD) or bulk population approach be adopted. In comparison, dominance effects would prove quite useful in hybrid wheat breeding programs.