1 Introduction

The Asymptotic Giant Branch (AGB) is a relatively short lived (e.g. Vassiliadis & Wood 1993), but decisive phase during the final evolutionary stages for stars with low to intermediate masses ($\approx$0.8-8 $M_{\odot}$). The vast majority of all stars, which leave the main sequence within a Hubble time, experience it after core helium-burning has ceased, and they appear as late-type giants in the Hertzsprung-Russell diagram (HRD).

The AGB phase is characterized by several important phenomena:
(i) The onset of repeated, explosive helium-burning in a shell [He-shell flashes, or thermal pulses (TP)] accompanied by deep convection, which leads to the production and dredge-up of carbon and heavy elements produced for instance by the s-process (e.g. Iben & Renzini 1983).
(ii) Pulsations with long periods (due to the enormous size and low density of AGB stars), usually combined with large size variations and the formation of shock fronts in the stellar atmosphere (e.g. Willson 1988). Depending on their pulsational properties, these objects are classified as Miras, semi-regular or irregular variables.
(iii) Finally, the development of strong stellar winds (with typical mass loss rates between 10^-8 and 10^-4 $M_{\odot}$yr^-1), which will eventually lead to a drastic change in stellar mass. This also produces a cool circumstellar envelope, where complex molecules and dust can form (Habing 1996).

Both their intrinsically high luminosity (with spectral energy distributions peaking in the red or infrared) and their well defined evolutionary stage make them important constituents and probes of extragalactic systems. Because of their high luminosity (up to a few 10⁴ $L_{\odot}$) AGB stars play an important role in studies of stellar populations (Lançon 1999). Due to their age they define highly relaxed subsystems of galaxies and are therefore interesting for work on galactic structure (Dejonghe & Caelenberg 1999). Finally, their mass loss significantly contributes to the enrichment of the interstellar medium (Habing 1996). Traditionally our knowledge of stellar populations in Local Group galaxies comes mainly from photometry of evolved giants. Even in the Large Magellanic Cloud (LMC) the observation of the main sequence is difficult due to crowding and confusion. Recent impressive observations (HST and ground-based) of Local Group galaxies complement our knowledge of other parts of the HRD (see e.g. Aparicio 1999). AGB stars represent important constituents of the intermediate age (1-10Gyr) stellar population in external galaxies and allow us to probe the star formation history for this time interval (Grebel 1999). AGB stars can be useful as distance estimators, too. Not only the relatively well defined period-luminosity (PL) relation of Mira variables, but also the narrow luminosity function of carbon stars can be used for this purpose.

On the other hand, extragalactic studies are important for our understanding of stellar evolution on the AGB itself (Zijlstra 1999). Extragalactic systems with their often well defined distances, metallicities, and star formation histories provide important tests for theoretical models by limiting the parameter space. Starting with an oxygen-rich ( ${\rm C/O}<1$) atmosphere at the onset of the AGB evolution, stars within the mass range of $\approx$1.5-4$M_{\odot}$can become carbon-rich ( ${\rm C/O}>1$) during the TP-AGB phase, i.e. the spectral type changes from M to S ( ${\rm C/O}\approx 1$) and finally to C. Among the most interesting AGB problems addressable by extragalactic research is the formation of these carbon-stars (e.g. the lower and upper mass limit). Another very important problem is the dependence of mass loss on mass, metallicity, and evolutionary age. By observing populations of different metallicity some light can be shed on these and other questions.

In general, large samples of AGB stars are needed for most investigations of their general properties (e.g. for a distance estimation from the C-star luminosity function). However, typically less than 10 C-stars are known in each of even the nearest satellite galaxies (see e.g. Groenewegen 1999, and references therein). In M 31 (the Andromeda galaxy) fewer than 250 C-stars have been identified, whereas some 10⁴ are expected from a comparison with the LMC (Brewer et al. 1995). Only the LMC, the SMC, and the Fornax dwarf galaxy can be called "well studied'' in this respect (e.g. Azzopardi 1999; Cioni et al. 2000).

Therefore, the efficient detection and characterization of such objects in extragalactic systems is essential for all the above mentioned studies.