Our recent extended peak resolution equation of capillary electrophoresis has been combined with the multiple equilibria-based electrophoretic mobility model of chiral separations to describe peak resolution as a function of the composition of the background electrolyte (pH and the beta-cyclodextrin concentration) and a function of the operating variables (effective portion of the applied potential, dimensionless electroosmotic flow coefficient). Using the previously determined model parameters, the resolution surfaces were calculated for a Type I chiral separation (ibuprofen), and a Type III chiral separation (homatropine). In Type I separations resolution can be obtained only over a narrow pH range in the vicinity of the pK(a) value, and above a minimum value, the concentration of beta-cyclodextrin plays a lesser role. In Type III separations, the pH- and beta-cyclodextrin concentration-dependent resolution surface has two lobes, on which the migration order of the enantiomers is opposite. This can be an advantage in trace component analysis. In both Type I and Type III separations, peak resolution varies strongly with the dimensionless electroosmotic flow coefficient when its value is changed in the -1 to 1 range. The loci of the pH-dependent and the beta-cyclodextrin concentration-dependent resolution maxima do not shift significantly when the dimensionless electroosmotic flow coefficient is changed. This fact provides the analyst with an additional resolution enhancement tool that does not alter the selectivity of the separation. The utility of the model and its theoretical predictions has been demonstrated by comparing measured and calculated R(s) values for ibuprofen and homatropine.