We present optical spectra for a representative sample of 27 nearby (z < 0.2) Two Micron All Sky Survey (2MASS)-selected active galactic nuclei (AGN) with red near-infrared colours (J - KS ≳ 2.0). The spectra were taken with the ISIS spectrograph on the William Herschel Telescope with the aim of determining the nature of the red 2MASS AGN, in particular whether they are young quasars obscured by their natal cocoons of gas and dust. We compare our findings with those obtained for comparison samples of PG quasars and unobscured type 1 AGN. The spectra show a remarkable variety, including moderately reddened type 1 objects (45 per cent), type 1 objects that appear similar to traditional ultraviolet (UV)-/optical-selected AGN (11 per cent), narrow-line type 1 Seyfert AGN (15 per cent), type 2 AGN (22 per cent) and H II/composite objects (7 per cent). The high Balmer decrements that we measure in many of the type 1 objects are consistent with their red J - KS colours being due to moderate levels of dust extinction (0.2 < E(B - V) < 1.2). However, we measure only modest velocity shifts and widths for the broader [O III]λ5007 emission-line components that are similar to those measured in the comparison samples. This suggests that the outflows in the red 2MASS objects are not unusual compared with those of optical-/UV-selected AGN of similar luminosity. In addition, the Eddington ratios for the 2MASS sample are relatively modest. Overall, based on their optical spectra, we find no clear evidence that the population of red, 2MASS-selected AGN at low redshifts represents young quasars. Most plausibly, these objects are normal type 1 AGN that are moderately obscured by material in the outer layers of the circumnuclear tori or in the discs of the host galaxies.