Following nutrient ingestion, glucagon-like peptide 1 (GLP-1) is secreted from intestinal L-cells and mediates anti-diabetic effects, most notably stimulating glucose-dependent insulin release from pancreatic β-cells but also inhibiting glucagon release, promoting satiety and weight reduction and potentially enhancing or preserving β-cell mass. These effects are mediated by the GLP-1 receptor (GLP-1R), which is a therapeutic target in type 2 diabetes. Although agonism at the GLP-1R has been well studied, desensitisation and resensitisation are perhaps less well explored. An understanding of these events is important, particularly in the design and use of novel receptor ligands. Here, using either HEK293 cells expressing the recombinant human GLP-1R or the pancreatic β-cell line, INS-1E with endogenous expressesion of the GLP-1R, we demonstrate GLP-1R desensitisation and subsequent resensitisation following removal of extracellular GLP-1 7-36 amide. Resensitisation is dependent on receptor internalisation, endosomal acidification and receptor recycling. Resensitisation is also regulated by endothelin-converting enzyme-1 (ECE-1) activity, most likely through proteolysis of GLP-1 in endosomes and the facilitation of GLP-1R dephosphorylation and recycling. Inhibition of ECE-1 activity also increases GLP-1-induced activation of extracellular signal-regulated kinase and generation of cAMP, suggesting processes dependent upon the lifetime of the internalised ligand–receptor complex.