Infrared J and K photometry has been obtained of all red giants in the half square degree region of the LMC bar searched for variables using the MACHO database byWood et al. (1999). The K–log P diagram shows the five distinct period–luminositysequences which are also evident in the MACHO photometry. The K–log P plot allowsidentification of the Mira sequence from among the five observed sequences. As shown in Wood et al. (1999), comparison of observed periods, luminosities and period ratios with theoretical models identifies Miras unambiguously as radial fundamental mode pulsators, while semi-regular variables can be pulsating in the first, second or third overtone, or even the fundamental mode. All these variables lie on just three of the five distinct sequences, and they all appear to be on the AGB. The nature of the variability of stars on the other two sequences is currently unknown. Possibilities include contact and semi-detached binaries, rotating stars with giant star spots, episodic dust formation, rotationally stabilised non-radial g− modes and strange pulsation modes caused by convection–pulsation interaction. These possibilities are discussed.