New almost-degenerate charged and neutral heavy leptons are a feature of a number of theories of physics beyond the Standard Model. The prospects for detecting these at the Large Hadron Collider using a time-of-flight technique are considered, along with any cosmological or experimental constraints on their masses. Based on a discovery criterion of 10 detected exotic leptons we conclude that, with an integrated luminosity of 100 fb-1, it should be possible to detect such leptons provided their masses are less than 950 GeV. It should also be possible to use the angular distribution of the produced particles to distinguish these exotic leptons from supersymmetric scalar leptons, at a better than 90% confidence level, for masses up to 580 GeV.