Photometric data on 17 binary near-Earth asteroids (15 of them are certain detections, two are probables) were analysed and characteristic properties of the near-Earth asteroid (NEA) binary population were inferred. We have found that binary systems with a secondary-to-primary mean diameter ratio D/D⩾0.18 concentrate among NEAs smaller than 2 km in diameter; the abundance of such binaries decreases significantly among larger NEAs. Secondaries show an upper size limit of D=0.5-1 km. Systems with D/D⩽0.5 are abundant but larger satellites are significantly less common. Primaries have spheroidal shapes and they rotate rapidly, with periods concentrating between 2.2 to 2.8 h and with a tail of the distribution up to ∼4 h. The fast rotators are close to the critical spin for rubble piles with bulk densities about 2 g/cm 3. Orbital periods show an apparent cut-off at P∼11 h; closer systems with shorter orbital periods have not been discovered, which is consistent with the Roche limit for strengthless bodies. Secondaries are more elongated on average than primaries. Most, but not all, of their rotations appear to be synchronized with the orbital motion; nonsynchronous secondary rotations may occur especially among wider systems with P>20 h. The specific total angular momentum of most of the binary systems is similar to within ±20% and close to the angular momentum of a sphere with the same total mass and density, rotating at the disruption limit; this suggests that the binaries were created by mechanism(s) related to rotation near the critical limit and that they neither gained nor lost significant amounts of angular momentum during or since formation. A comparison with six small asynchronous binaries detected in the main belt of asteroids suggests that the population extends beyond the region of terrestrial planets, but with characteristics shifted to larger sizes and longer periods. The estimated mean proportion of binaries with D/D⩾0.18 among NEAs larger than 0.3 km is 15±4%. Among fastest rotating NEAs larger than 0.3 km with periods between 2.2 and 2.8 h, the mean proportion of such binaries is (66 +10-12)%.