Background and aims - The evolutionary history of Amazonia's hyperabundant tropical tree species. also known as "hyperdominant" species, remains poorly investigated. We assessed whether the hyperdominant Eschweilera coriacea (DC.) S.A.Mori (Lecythidaceae) represents a single genetically cohesive species, and how its genetic constitution relates to other species from the same Glade with which it occurs sympatrically in French Guiana. Methods - We sampled 152 individuals in nine forest sites in French Guiana, representing 11 species of the genus Eschweilera all belonging to the Parvifolia Glade, with emphasis on E. coriacea. Samples were genotyped at four simple sequence repeat (SSR) markers. We delimited gene pools, i.e.. genetically coherent putative taxa, using STRUCTURE software and principal component analysis. We compared the genetic assignment of individuals with their morphological species determination and estimated genetic diversity and differentiation for gene pools and species. We also estimated genome size using flow cytometry. Key results - SSR profiles commonly displayed up to four alleles per genotype, suggesting that the investigated Eschweilera species bear a paleopolyploid signature. Flow cytometty suggested that the studied species are diploid with haploid genome sizes of 871-1046 Mbp. We detected five gene pools and observed a good correspondence between morphological and genetic delimitation for Eschweilera sagotiana Miers and the undescribed morphospecies E. sp. 3 (which resembles E. grandiflora (Aubl.) Sandwith), and to a lesser extent for E. decolorans Sandwith and E. micrantha (O.Berg) Miers. Eschweilera coriacea was the most genetically diverse species and included individuals assigned to each gene pool. Conclusions - We found no conclusive evidence for cryptic species within E. coriacea in French Guiana. SSRs detected fewer gene pools than expected based on morphology in the Parvifolia Glade but discriminated evolutionary relationships better than available plastid markers. A positive trend between demographic abundance of species and allelic richness illustrates that hyperdominants may have a high evolutionary potential. This hypothesis can be tested using more powerful genomic data in combination with tree phenotypic trait variation and characterization of niche breadth, to enhance our understanding of the causes of hyperdominance in Amazonian trees.