Persistent nonphotochemical and photochemical hole burning of the S-0-->S-1 origin absorption bands of chromophores in amorphous hosts such as glasses, polymers and proteins at low temperatures have been used to address a number of problems that range from structural disorder and configurational tunneling to excitation energy transfer and charge separation in photosynthetic complexes. Often the hole burned spectra are interfered by photoproduct (antihole) absorption. To date there has been no systematic approach to modeling hole burned spectra and the dispersive kinetics of zero-phonon hole growth that accounts for the antihole. A "master" equation that does so is presented. A key ingredient of the equation is a time-dependent, two-dimensional site excitation frequency distribution function (SDF) of the zero-phonon lines. Prior to hole burning (t=0) the SDF is that of the educt sites. For t>0 the SDF describes both educt and photoproduct sites and allows for burning of the latter that revert to the educt sites from which they originate (light-induced hole filling). Our model includes linear electron-phonon coupling and the three distributions that lead to dispersive hole growth kinetics, the most important of which is the distribution for the parameter lambda associated with tunneling between the bistable configurations of the chromophore-host system that are interconverted by hole burning. The master equation is successfully applied to free base phthalocyanine (Pc) in hyperquenched glassy ortho-dichlorobenzene (DCB) at 5 K. The mechanism of hole burning is photochemical and involves tautomerization of the two protons at the center of the macrocycle (Pc) that occurs in the S-1(Q(x)) and/or T-1(Q(x)) state of Pc. A single set of parameter values (some of which are determined directly from the hole burned spectra) provides a satisfactory description of the dependence of the hole burned spectra and hole growth kinetics on the location of the burn frequency within the inhomogeneously broadened Q(x) absorption band. The hole growth kinetics are found to be quite highly dispersive, although to a lesser degree than the kinetics for free base phthalocyanine tetrasulphonate in hyperquenched glassy water [Reinot , J. Lumin. 98, 183 (2002)]. The dispersion is attributed to structural heterogeneity of solvent molecules in the inner shell that leads to a distribution of chromophore-host interactions that affect the height of the barrier separating the two tautomers. The new master equation should also prove useful with no additional assumptions or modifications for interpretation of nonphotochemical hole burned spectra. (C) 2003 American Institute of Physics.