Glucose phosphorylation capacity is known to be in excess of glucose flux in Saccharomyces cerevisiae wild type but not in a mutant strain lacking the two hexokinases but still having glucokinase. Nonetheless, we show here that in the latter strain, as in the wild type, the internal concentration of glucose is apparently low during growth on glucose and that additional glucokinase activity does not increase glucose flux. The glucokinase-dependent strain accumulates substantial amounts of glucose internally in batch culture after exhaustion of glucose, as well as from maltose. In both of these situations, low concentrations of radioactive glucose provided to the medium are used with incomplete, if any, mixing with the internal pool. Furthermore, in contrast to activity of hexokinase and other enzymes, little glucokinase activity is revealed by toluene treatment of cells. These results may point to a connection between glucose entry and its phosphorylation by glucokinase, but separate explanations for the various findings are also possible.