  We present new spectroscopic observations of Mkn 309, a starburst galaxy with
one of the largest WR populations known. A highly super solar metallicity is
derived. Using additional objects we analyse a sample of five metal-rich WR
galaxies with the main goal of constraining the basic properties of the massive
star populations (IMF slope, M_up) and the star formation history (age, burst
duration) of these objects by quantitative comparisons with evolutionary
synthesis models. The following main results are obtained: 1) The observations
are well explained by extended bursts of star formation or a superposition of
several bursts. Ages and burst durations are estimated. This naturally explains
both the observed WR populations (including WN and WC stars) and the presence
of red supergiants. 2) The fitted SEDs indicate that the stellar light suffers
from a smaller extinction than that of the gas, confirming independent earlier
findings. 3) All the considered observational constraints are compatible with a
Salpeter IMF extending to masses >~ 40 Msun. Adopting a conservative approach
we derive a LOWER LIMIT of Mup >~ 30 Msun for the Salpeter IMF. From more
realistic assumptions on the metallicity and SF history we favour a lower limit
Mup >~ 30-40 Msun, which is also in agreement with Hbeta equivalent width
measurements of metal-rich HII regions in spiral galaxies indicating an upper
mass cut-off of at least ~ 35 - 50 Msun. Steep IMF slopes (alpha >~ 3.3) are
very unlikely. (abridged/modified abstract)
