In the period - luminosity (PL) diagram of pulsating red giants in the
LMC, five sequences can be identified. Recent observations have refined this initial
finding and many more sequences have been discovered. The two main sequences
comprise Miras and semiregulars which are stars in the fundamental and
first-overtone radial pulsation modes. Carbon-rich and oxygen-rich Miras form distinct
sub-sequences as do C-rich and O-rich semiregulars. At least four further sequences
roughly parallel to the Mira and semiregular sequences have been identified
which may correspond to higher overtone radial modes. The stars which populate
these sequences are the OGLE Small Amplitude Red Giants (OSARGs). The
OSARG sequences themselves are resolved into further subsequences of asymptotic
giant branch stars and stars below the tip of the red giant branch. It is likely that
nonradial modes are present in OSARGs as the Petersen diagram for these stars
show some period ratios close to unity. In addition to these complex sequences of
pulsating stars, there are two more sequences in the PL diagram. One sequence can
be shown to consist of contact binaries. The nature of stars in the other sequence is
a mystery. These stars have long secondary periods which do not seem to be due
to pulsation. Although it is certain that convection is responsible for driving pulsation
in these stars, the precise driving mechanism is not understood. It is possible
that in the low-amplitude stars pulsation may be driven stochastically.
