Post-translational modifications alter the properties of proteins through the cleavage of peptide bonds or the addition of a modifying group to one or more amino acids. These modifications allow proteins to perform their primary biological functions, but single-protein studies of post-translational modifications have been hindered by a lack of suitable analysis methods. Here, we show that single amino acids can be identified using electron tunnelling currents measured as the individual molecules pass through a nanoscale gap between electrodes. We identify 12 different amino acids and the post-translational modification phosphotyrosine, which is involved in the process that switches enzymes on and off. Furthermore, we show that the conductance measurements can be used to partially sequence peptides of an epidermal growth factor receptor substrate, and can discriminate a peptide from its phosphorylated variant.