RNA molecules undergo a vast array of chemical post-transcriptional modifications (PTMs) that can affect their structure and interaction properties. In recent years, a growing number of PTMs have been successfully mapped to the transcriptome using experimental approaches relying on high-throughput sequencing. Oxford Nanopore direct-RNA sequencing has been shown to be sensitive to RNA modifications. We developed and validated Nanocompore, a robust analytical framework that identifies modifications from these data. Our strategy compares an RNA sample of interest against a non-modified control sample, not requiring a training set and allowing the use of replicates. We show that Nanocompore can detect different RNA modifications with position accuracy in vitro, and we apply it to profile m6A in vivo in yeast and human RNAs, as well as in targeted non-coding RNAs. We confirm our results with orthogonal methods and provide novel insights on the co-occurrence of multiple modified residues on individual RNA molecules.