We present new spectroscopic observations of Mkn 309 , a starburst galaxy with one of the largest WR populations known .
A highly super solar metallicity of 12 + \log ( O/H ) \sim 9.3–9.4 is derived .
Using additional objects from Guseva et al .
( 2000 ) we analyse a sample of five metal-rich ( [ O/H ] > 0 ) 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 :

• The observations are well explained by extended bursts of star formation with durations \Delta t \sim 4–10 Myr seen at ages of 7–15 Myr or a superposition of several bursts with age differences of \sim 4–10 Myr including a young ( \la 5 Myr ) burst .
This naturally explains both the observed WR populations ( including WN and WC stars ) and the presence of red supergiants .
The burst durations , somewhat longer compared to those derived in other WR galaxies using the same models ( Schaerer et al .
1999a ) , are plausible in view of the physical sizes of the observed regions and the nature and morphology of our objects ( nuclear starbursts ) , and pose no fundamental physical problem .

• The SEDs in the optical range are very well reproduced for all objects , provided the stellar light suffers from a smaller extinction than that of the gas ( derived from the Balmer decrement ) .
This confirms earlier findings from studies combining UV–optical data of other starburst galaxies .

• All the considered observational constraints are compatible with a Salpeter IMF extending to masses M _ { up } \ga 40 M _ { \odot } .
Adopting a conservative approach we derive a lower limit of M _ { up } \ga 30 M _ { \odot } for the Salpeter IMF .
From more realistic assumptions on the metallicity and SF history we favour a lower limit M _ { up } \ga 30–40 M _ { \odot } , which is also in agreement with H \beta equivalent width measurements of metal-rich H ii regions in spiral galaxies indicating an upper mass cut-off of at least \sim 35 – 50 M _ { \odot } .
Steep IMF slopes ( \alpha \ga 3.3 ) are very unlikely .

The uncertainties of our results are discussed .
We compare our findings to other work on massive star populations and the IMF in similar environments .
We stress the importance of direct analysis of stellar populations compared to other indirect methods based on properties of ionized gas to constrain the IMF in metal-rich starbursts .