Preserving hue is an important issue for color image processing. In order to preserve hue, color image processing is often carried out in HSI or HSV color space which is translated from RGB color space. Transforming from RGB color space to another color space and processing in this space usually generate gamut problem. We propose image enhancement methods which conserve hue and preserve the range (gamut) of the R, G, B channels in this paper. First we show an intensity processing method while preserving hue and saturation. In this method, arbitrary grayscale transformation functions can be applied to the intensity component. Next, a saturation processing method while preserving hue and intensity is proposed. Arbitrary gray-scale transform methods can be also applied to the saturation component. Two processing methods are completely independent. Therefore, two methods are easily combined by applying two processing methods in succession. The combination method realizes the hue-preserving color image processing with a high arbitrariness without gamut problem. Furthermore, the concrete enhancement algorithm based on the proposed processing methods is proposed. Numerical results confirmour theoretical results and show that our processing algorithm performs much better than the conventional hue-preserving methods.