Tree stems in tropical peat swamp forests are known as considerable methane (CH4) emitters; however, little is known about their carbon dioxide (CO2) and nitrous oxide (N2O) exchange. Differences between species, especially the role of palm stems in the exchange of greenhouse gasses, have remained largely unknown. We measured stem CO2, CH4, and N2O fluxes from the different heights of widely spread aguaje palms (Mauritia flexuosa) and boarwoods (Symphonia globulifera) and the soil beneath the same trees in a Peruvian Amazon palm swamp using a static closed chamber technique from September 2019 to March 2020. The tree stems were the net emitters of CO2 and CH4 but occasionally showed low N2O uptake. We found the highest stem CH4 emissions (average ± SE) from palm stems of the height of 80 cm (1,601 ± 165.9 μg C m–2 h–1), which are more than 300 times greater compared to the highest fluxes from boarwood stems, at the height of 30 cm (5.12 ± 1.27 μg C m–2 h–1). The average soil CH4 flux was 3,618 ± 465 μg C m–2 h–1. Whereas N2O fluxes from the stems were negligible, the average N2O fluxes from soils beneath the same trees were relatively high, ranging from 53.75 ± 24.04 (close to boarwood trees) to 143.4 ± 68.43 (close to palms) μg N m–2 h–1. While roughly upscaling tree-level fluxes to the stand level of 27,732 km2 of palm swamp in the Pastaza-Marañon foreland basin, these forests are net annual emitters of CH4 and N2O (897 Gg C y–1 and 24 Gg N y–1, respectively). These results highlight the necessity to study this kind of ecosystem more intensely.