Color difference equations based on the CIECAM02 color appearance model and IPT color space have been developed to fit experimental data. There is no color space in which these color difference equations are Euclidean, e.g. describe distances along a straight line. In this thesis, Euclidean color spaces have been derived for the CIECAM02 and IPT color difference equations, respectively, so that the color difference can be calculated as a simple color distance. Firstly, the Euclidean line element was established, from which terms were derived for the new coordinates of lightness, chroma, and hue angle. Then the spaces were analyzed using performance factors and statistics to test how well they fit various data. The results show that the CIECAM02 Euclidean color space has performance factors similar to the optimized CIECAM02 color difference equation. To statistical significance, the CIECAM02 Euclidean color space had superior fit to the data when compared to the CIECAM02 color difference equation. Conversely, the IPT Euclidean color space performed poorer than the optimized IPT color difference equation. The main reason is that the line element for the lightness vector dimension could not be directly calculated so an approximation was used. To resolve this problem, a new IPT color difference equation should be designed such that line elements can be established directly.