This article describes two methods for N-dimensional device color gamut representation: one is for gamut surface description, the other for gamut volume description. Both methods combine analytical and geometrical approaches. These methods can be applied to any colorant spaces such as 3-Dimensional RGB or CMY, 4-Dimensional CMYK, 6-Dimensional Hexachrome((R)) (CMYKOG), as well as the 14-Dimensional PANTONE MATCHING SYSTEM (R). The N-Dimensional gamut surface description method divides the gamut staface into many subsurfaces with only two-colorant variables. The gamut volume description first divides the whole gamut volume into 3D cubes without overlaps; then an analytical, geometrical, or interpolation method can be applied to each cube. Finally, all subgamuts are united to create the whole gamut. The analytical approach or interpolation technology is applied into these methods to predict unknown colors. The result is highly accurate with an average error less than 0.11 Delta E in CIEDE2000 for CMYK space and less than 0.56 Delta E in CIEDE2000 for higher dimensions. (c) 2007 Wiley Periodicals, Inc.