We present the results of a near-infrared monitoring programme of a selected sample of stars, initially suspected to be Mira variables and OH/IR stars, covering more than a decade of observations. The objects monitored cover the typical range of IRAS colours shown by O-rich stars on the asymptotic giant branch and show a surprisingly large diversity of variability properties. Sixteen objects are confirmed as large-amplitude variables. Periods between 360 and 1800d and typical amplitudes 1m ⪉ Δ K ⪉ 2m could be determined for nine of them. In three light curves, we find a systematic decrease in the mean brightness, and two light curves show pronounced asymmetry. One source, IRAS 07222-2005, shows infrared colours typical of Mira variables, but it pulsates with a much longer period (≈1200^d) than a normal Mira. Two objects are either close to (IRAS 03293+6010) or probably in (IRAS 18299-1705) the post-AGB phase. In IRAS 16029-3041 we found a systematic increase in the H-K colour of ≈1^m, which we interpret as evidence of a recent episode of enhanced mass loss. IRAS 18576+0341, a heavily obscured luminous blue variable was also monitored. The star showed a continued decrease in brightness over a period of 7 years (1995-2002).