We have studied the Lyα, Hβ, Hα, and Mg II λ2798 line profiles of the Seyfert 1 galaxy III Zw 2. The shapes of these broad emission lines show evidence of a multicomponent origin and also features that may be identified as the peaks due to a rotating disk. We have proposed a two-component broad-line region (BLR) model consisting of an inner Keplerian relativistic disk and an outer structure surrounding the disk. The results of the fitting of the four broad emission lines (BELs) considered here are highly consistent in both the inner and outer component parameters. Adopting a mass of ~2×108Msolar for the central object, we found that the outer radius of the disk is approximately equal for the four considered lines (~0.01 pc). However, the inner radius of the disk is not the same: 0.0018 pc for Lyα, 0.0027 pc for Mg II, and 0.0038 pc for the Balmer lines. This, as well as the relatively broad component present in the blue wings of the narrow [O III] lines, indicates stratification in the emission-line region. Using long-term Hβ observations (1972-1990, 1998) we found a flux variation of the BELs with respect to the [O III] lines.