We present a CCD photometric and mass function study of nine young Large Magellanic Cloud star clusters, namely NGC 1767, 1994, 2002, 2003, 2006, SL 538, NGC 2011, 2098 and 2136. BV RI data, reaching down to V∼ 21 mag, were collected from the 3.5-m NTT/EFOSC2 in subarcsec seeing conditions. For NGC 1767, 1994, 2002, 2003, 2011 and 2136, broad-band photometric CCD data are presented for the first time. Seven of the nine clusters have ages between 16 and 25 Myr, and the other two have ages of 32 ± 4 Myr (NGC 2098) and 90 ± 10 Myr (NGC 2136). For the seven youngest clusters, the age estimates based on a recent model and the integrated spectra are found to be systematically lower (∼10 Myr) than the present estimates. In the mass range ∼2–12 M⊙, the mass function slopes for eight out of nine clusters were found to be similar, with the value of γ ranging from −1.90 ± 0.16 to −2.28 ± 0.21. For NGC 1767 the slope is flatter, with γ=−1.23 ± 0.27. Mass segregation effects are observed for NGC 2002, 2006, 2136 and 2098. This is consistent with the findings of Kontizas and colleagues for NGC 2098. The presence of mass segregation in these clusters could be an imprint of the star formation process, as their ages are significantly smaller than their dynamical evolution time. The mean mass function slope of γ=−2.22 ± 0.16 derived for a sample of 25 young (≤100 Myr) dynamically unevolved Large Magellanic Cloud stellar systems provides support for the universality of the initial mass function in the intermediate-mass range ∼2–12 M⊙.