We estimate cluster ages from lithium depletion in five pre-main-sequence groups found within 100 pc of the Sun: TW Hydrae Association, Eta Chamaeleontis Cluster, Beta Pictoris Moving Group, Tucanae-Horologium Association and AB Doradus Moving Group. We determine surface gravities, effective temperatures and lithium abundances for over 900 spectra through least squares fitting to model-atmosphere spectra. For each group, we compare the dependence of lithium abundance on temperature with isochrones from pre-main-sequence evolutionary tracks to obtain model dependent ages. We find that the Eta Chamaelontis Cluster and the TW Hydrae Association are the youngest, with ages of 12+/-6 Myr and 12+/-8 Myr, respectively, followed by the Beta Pictoris Moving Group at 21+/-9 Myr, the Tucanae-Horologium Association at 27+/-11 Myr, and the AB Doradus Moving Group at an age of at least 45 Myr (where we can only set a lower limit since the models -- unlike real stars -- do not show much lithium depletion beyond this age). Here, the ordering is robust, but the precise ages depend on our choice of both atmospheric and evolutionary models. As a result, while our ages are consistent with estimates based on Hertzsprung-Russell isochrone fitting and dynamical expansion, they are not yet more precise. Our observations do show that with improved models, much stronger constraints should be feasible: the intrinsic uncertainties, as measured from the scatter between measurements from different spectra of the same star, are very low: around 10 K in effective temperature, 0.05 dex in surface gravity, and 0.03 dex in lithium abundance.

Accepted to ApJ, 15 pages, 8 colour figures