For many new display types the chromaticity coordinates of the primaries differ from those recommended by the EBU (European Broadcast Union). In order to identify optimal and acceptable ranges in which these primary colors may vary two studies were conducted: one related to the hue of the primaries (described in a previous paper) and one related to their saturation (this paper) and the results were combined. In the first experiment of this paper, observers set the saturation of either one primary (R, G, or B) or of all three primaries at the same time, to an optimum, for 7 different (natural) images. In the second experiment, the same observers decreased the saturation until they perceived the image as “just acceptable” (defined as “having natural colors given its content”). Both experiments were conducted on an LCD monitor and repeated later with a different set of subjects on a CRT monitor. The results of the experiments show that for optimal image quality the saturation of the red and green primaries of a display must be at least 90% (with respect to the EBU standard). For the blue primary it can be somewhat lower (at least about 70%). In the acceptance task observers were the least tolerant in accepting a saturation reduction of the red primary (to 70%) and the green primary (to 60%), but they were almost twice as tolerant for the blue primary (to 35%). Ellipses were fitted to the results of the hue and saturation studies in 1976 CIE (u'v') color space such that display manufactures can easily test whether the color reproduction of their displays is optimal, acceptable, or unacceptable with respect to reproducing natural colors.