We present intermediate dispersion optical spectroscopy for seven very low-mass stars in the α Per open cluster with spectral types between M3 and M6, including the brown dwarf candidate of Rebolo et al. (1992). Our radial velocity measurements are found to be generally consistent with the mean cluster velocity to within the measurement errors. Hα equivalent widths have been measured and compared to previous published data for other known members of the cluster. A turnover in chromospheric activity around spectral type M3-M4 is observed. The brown dwarf candidate, located in the cool side of the turnover, is confirmed to exhibit a strong Hα variability. It is the coolest α Per candidate member for which spectra are available and for which chromospheric activity has been measured. Using the LiI doublet at λ6707.8A, we derive upper limits to the atmospheric Li abundance in the sample and discuss them in the context of the most recent stellar evolutionary tracks. The non-detection of the Lii line in the spectrum of the brown dwarf candidate implies a mass greater than 0.08Msun_, and therefore it is not a substellar object. However, its position in the HR diagram implies that this star is indeed very close to the substellar limit.