Little is known about the prevalence, diversity, evolutionary processes, genomic structures and population dynamics of viruses in the divergent geminivirus lineage known as the capulaviruses. We determined and analyzed full genome sequences of 13 Euphorbia caput-medusae latent virus (EcmLV) and 26 Alfalfa leaf curl virus (ALCV) isolates, and partial genome sequences of 23 EcmLV and 37 ALCV isolates. While EcmLV was asymptomatic in uncultivated southern African Euphorbia caput-medusae, severe alfalfa disease symptoms were associated with ALCV in southern France. The prevalence of both viruses exceeded 10% in their respective hosts. Besides using patterns of detectable negative selection to identify ORFs that are probably functionally expressed, we show that ALCV and EcmLV both display evidence of inter-species recombination and biologically functional genomic secondary structures. Finally, we show that whereas the EcmLV populations likely experience restricted geographical dispersion, ALCV is probably freely moving across the French Mediterranean region.