By means of statistical analyses, we compute the luminosity function o
f galaxies in clusters and explore its dependence on cluster global pr
operties. The data consist of two different samples of southern cluste
rs with published redshifts, taken from the Abell cluster catalog and
the APM cluster catalog. Galaxy assignment to the clusters and their c
orresponding apparent magnitudes were derived from the Edinburgh-Durha
m Southern Galaxy catalogue. We have considered two limiting absolute
magnitudes, M <-16 and M <-17, comprising 16 and 55 clusters, respecti
vely. The galaxy luminosity function in clusters derived in this work
shows a large excess of faint galaxies compared with previous field de
terminations. In spite of their different identification procedures, w
e obtain similar galaxy luminosity functions in Abell and APM clusters
. A Schechter function with parameters Msimilar or equal to-20.0+/-0.
1 and alpha similar or equal to-1.4+/-0.1 provides a satisfactory st t
o the galaxy luminosity function of the sample of 55 clusters. We also
find a flatter galaxy luminosity function in poor clusters (alpha sim
ilar or equal to-1.2). We have computed errors through a Monte Carlo p
rocedure that considers different possible background corrections and
errors in the photometry. Besides providing reliable values of the unc
ertainties in the luminosity function fitting parameters, this method
poses confident limits on the effects of possible systematics. Our res
ults strongly argue against a universal galaxy luminosity function. Th
e high relative frequency of faint galaxies in rich clusters reported
in this work may provide constraints on models for the origin and evol
ution of galaxies.