We present spectra of 59 nearby star candidates, M dwarfs and white dwarfs, previously identified using high proper motion catalogues and the DENIS database. We review the existing spectral classification schemes and spectroscopic parallax calibrations in the near-infrared J band and derive spectral types and distances of the nearby candidates. Forty-two stars have spectroscopic distances smaller than 25pc, three of them being white dwarfs. Two targets lie within 10pc, one M8 star at 10.0pc (APMPM J0103-3738), and one M4 star at 8.3pc (L 225-57). One star, LHS 73, is found to be among the few subdwarfs lying within 20pc. Furthermore, together with LHS 72, it probably belongs to the closest pair of subdwarfs we know.