Adductomics studies are used for the detection and characterization of various chemical modifications (adducts) of nucleic acids and proteins. The advancements in liquid chromatography coupled with high-resolution tandem mass spectrometry (HRMS/MS) have resulted in efficient methods for qualitative and quantitative adductomics. We developed an HRMS-based method for the simultaneous analysis of RNA and DNA adducts in a single run and demonstrated its application using Baltic amphipods, useful sentinels of environmental disturbances, as test organisms. The novelty of this method is screening for RNA and DNA adducts by a single injection on an Orbitrap HRMS instrument using full scan and data-independent acquisition. The MS raw files were processed with an open-source program, nLossFinder, to identify and distinguish RNA and DNA adducts based on the characteristic neutral loss of ribonucleosides and 2′-deoxyribonucleosides, respectively. In the amphipods, in addition to the nearly 150 putative DNA adducts characterized earlier, we detected 60 putative RNA adducts. For the structural identification of the detected RNA adducts, the MODOMICS database was used. The identified RNA adducts included simple mono- and dimethylation and other larger functional groups on different ribonucleosides and deaminated product inosine. However, 54 of these RNA adducts are not yet structurally identified, and further work on their characterization may uncover new layers of information related to the transcriptome and help understand their biological significance. Considering the susceptibility of nucleic acids to environmental factors, including pollutants, the developed multi-adductomics methodology with further advancement has the potential to provide biomarkers for diagnostics of pollution effects in biota.