This paper describes the analysis of UVES and GIRAFFE spectra acquired by the Gaia-ESO Public Spectroscopic Survey in the fields of young clusters whose population includes pre-main sequence (PMS) stars. Both methods that have been extensively used in the past and new ones developed in the contest of the Gaia-ESO survey enterprise are available and used. The internal precision of these quantities is estimated by inter-comparing the results obtained by such different methods, while the accuracy is estimated by comparison with independent external data, like effective temperature and surface gravity derived from angular diameter measurements, on a sample of benchmarks stars. Specific strategies are implemented to deal with fast rotation, accretion signatures, chromospheric activity, and veiling. The analysis carried out on spectra acquired in young clusters fields during the first 18 months of observations, up to June 2013, is presented in preparation of the first release of advanced data products. Stellar parameters obtained with the higher resolution and larger wavelength coverage from UVES are reproduced with comparable accuracy and precision using the smaller wavelength range and lower resolution of the GIRAFFE setup adopted for young stars, which allows us to provide with confidence stellar parameters for the much larger GIRAFFE sample. Precisions are estimated to be $approx$ 120 K r.m.s. in Teff, $approx$0.3 dex r.m.s. in logg, and $approx$0.15 dex r.m.s. in [Fe/H], for both the UVES and GIRAFFE setups.
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