The instrument configuration and performance characteristics of the X-ray imaging telescopes on EXOSAT are described. The instrument comprises two fully independent Wolter I imaging telescopes. Each telescope can be used in either of two principal modes: (i) an imaging mode with either a position sensitive proportional counter or a channel multiplier array plate in the focal plane, (ii) a spectrometer mode which features a 500 lines/mm and/or a 1000 lines/mm transmission grating as dispersive element. Preliminary results from the calibration of the fully integrated experiment indicate an ultimate angular resolution of 8.5 arc sec full width at half maximum or 17.5 arc sec half-power beam width. The ultimate wavelength resolution in the spectrometer mode ranges from 1Å for wavelengths below 50Å, to 5Å at wavelengths near 300Å. A method for estimating the telescope performance is given which reasonably accounts for the influence of the X-ray source spectrum and the degree of interstellar absorption on the counting statistics. A comparison between EXOSAT and the EINSTEIN telescope in terms of band width/resolution and minimum source detectability shows an enhanced potential for EXOSAT relative to EINSTEIN for sources with T ≦ 107K and low column densities (< 4 × 1020cm-2) and a reduced potential for sources with hard, or heavily cut-off, spectra.