Given the spectral mechanism of color constancy (Part I of this series), the remaining nonspectral mechanism is formulated here in Part II by the constraint of correlation with known spectral illuminant-invariant functions, i.e., invariant wavelength ratios between Constant lilies, which plot straight parallel lilies in the plane of, wavelength and reciprocal illuminant color temperature (MK-1). The same is assumed to apply to nonspectral constant hues in the same plane and dominant wavelength scale extended to cover the nonspectrals (see accompanying article "Relative wavelength metric for the complete hue cycle ..."). To simplify analysis, stimuli are optimal aperture colors: their monochromatic stimuli lie between 442 and 613 nm, common boundaries with optimal compound stimuli (nonspectrals). It is shown that the wavelengths and invariant ratios of spectral constant lilies can be formulated exactly (+/- 0.5%) from the ratios of all harmonic period. which shafts wavelength with MK-1. The formula implies this color-constant hue cycle is isomorphic across illuminants and allows prediction of nonspectral constant hues. To identify these colorimetrically, their spectral complementary wavelenghts ore specified for various illuminants. This completes the global color constancy mechanism for the illuminant color temperature range 2800 to 25,000 K. (C) 2010 Wiley Periodicals, Inc. Col Res Appl, 35, 134-144, 2010: Pubished online 7 January 2010 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20535