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Aims: To investigate variability and to model the pulsational behaviour ofAGB variables in the intermediate-age LMC cluster NGC 1846.  Methods: Our own photometric monitoring has been combined with data from theMACHO archive to detect 22 variables among the cluster's AGB stars and toderive pulsation periods. According to the global parameters of the cluster weconstruct pulsation models taking into account the effect of the C/O ratio onthe atmospheric structure. In particular, we have used opacities appropriatefor both O-rich stars and carbon stars in the pulsation calculations.  Results: The observed P-L-diagram of NGC 1846 can be fitted using a mass ofthe AGB stars of about 1.8 M$_{\sun}$. We show that the period of pulsation isincreased when an AGB star turns into a carbon star. Using the mass on the AGBdefined by the pulsational behaviour of our sample we derive a cluster age of$1.4\times10^{9}$ years. This is the first time the age of a cluster has beenderived from the variability of its AGB stars. The carbon stars are shown to bea mixture of fundamental and first overtone radial pulsators.

The AGB stars of the intermediate-age LMC cluster NGC 1846 Variability and age determination