  The period-luminosity relation of Miras and semiregular variables in the
Large Magellanic Cloud and in the Galaxy is used to locate their instability
domain in the Hertzsprung-Russell diagram. We take advantage of the
considerable width in luminosity of the relation at given period to assign
masses to the observed long-period variables using stellar models on the the
asymptotic giant branch and nonadiabatic pulsation computations. We study the
sensitivity to chemical abundance of the position of the instability region on
the Hertzsprung-Russell diagram. The mass function of the long-period variables
along the AGB is discussed for Galactic and LMC variables. Finally, we
contribute to the dispute on the pulsation mode of Miras and lend support to
the view that, for most of the Mira variables, the pulsation in the fundamental
mode is more likely.
