CYCLOIDEA (CYC) and DICHOTOMA (DICH) are paralogous genes that determine adaxial (dorsal) flower identity in the bilaterally symmetric flowers of Antirrhinum majus (snapdragon). We show here that the duplication leading to the existence of both CYC and DICH in Antirrhinum occurred before the radiation of the Antirrhineae (the tribe to which snapdragon belongs). We find no additional gene duplications within Antirrhineae. Using explicit codon-based models of evolution in a likelihood framework, we show that patterns of molecular evolution after the duplication that gave rise to CYC and DICH are consistent with purifying selection acting at both loci, despite their known functional redundancy in snapdragon. However, for specific gene regions, purifying selection is significantly relaxed across DICH lineages, relative to CYC lineages. In addition, we find evidence for relaxed purifying selection along the lineage leading to snapdragon in one of two putative functional domains of DICH. A model of selection accounting for the persistence of paralogous genes in the absence of diversifying selection is presented. This model takes into account differences in the degree of purifying selection acting at the two loci and is consistent with subfunctionalization models of paralogous gene evolution.