To study the dependence of the perceptual achromatic color onthe lightness level and the viewing illuminations, the four lightness levels of thenear achromatic colors and the three viewing illuminations are prepared. Thepsychological assessment is to classify the near achromatic colors at the samelightness level into two categories. The one category is to accept as the achromaticcolor, and the other to reject as the achromatic color.　The acceptance as the achromaic color (white, light gray, medium gray, dark gray)depends on the viewing illuminations. At the low color temperature (incandescentlamp), the bluish colors are more acceptable. I assume that the psychologicalstructure of the judgement of the achromaticity is the same at lightness levels.