A magnet spectrograph, with visual detectors, and arrays of diffusedlight Cerenkov detectors at the Haverah Park Cosmic Ray Station have been used to determine the momenta, the signs and the densities of muons in large extensive air showers. The observational data cover the momentum range 1-100 Gev/c, and refer to muons at distances of 10-800 m from the cores of showers of size 10⁵-10⁸ particles. The measurements are used to compute the spectra by a method which involves only very broad assumptions about the shape of the spectra. The spectra are presented in the form of the integral and differential muon densities as functions of momentum and core distance.The results are compared with the magnet spectrograph measurements of Bennett and Greisen, and good agreement is found where the data are comparable. The empirical relation suggested by Greisen fits the present results well, but the absolute number of muons given by the relation is rather smaller than found here. Comparison is also made with other types of experiment and fair agreement is found in certain cases.An attempt is made to check the preliminary predictions of recent theoretical models of the nuclear cascade by Hillas and Holyoak et al. Some agreement is found, but both of these theories predict too few high-energy muons at large distances from the core. A theoretical interpretation by Khrenov of experimental data on the lateral distribution of muons also predicts muon densities at large distances from the core which are much lower than found here.