Among the myriad of data collected by the ESA Gaia satellite, about 150 million spectra will be delivered by the Radial Velocity Spectrometer (RVS) for stars as faint as G_RVS~16. A specific stellar parametrization will be performed for most of these RVS spectra. Some individual chemical abundances will also be estimated for the brightest targets. We describe the different parametrization codes that have been specifically developed or adapted for RVS spectra within the GSP-spec working group of the analysis consortium. The tested codes are based on optimization (FERRE and GAUGUIN), projection (MATISSE) or pattern recognition methods (Artificial Neural Networks). We present and discuss their expected performances in the recovered stellar atmospheric parameters (Teff, log(g), [M/H]) for B- to K- type stars. The performances for the determinations of [alpha/Fe] ratios are also presented for cool stars. For all the considered stellar types, stars brighter than G_RVS~12.5 will be very efficiently parametrized by the GSP-spec pipeline, including solid estimations of [alpha/Fe]. Typical internal errors for FGK metal-rich and metal-intermediate stars are around 40K in Teff , 0.1dex in log(g), 0.04dex in [M/H], and 0.03dex in [alpha/Fe] at G_RVS=10.3. Similar accuracies in Teff and [M/H] are found for A-type stars, while the log(g) derivation is more accurate. For the faintest stars, with G_RVS>13-14, a spectrophotometric Teff input will allow the improvement of the final GSP-spec parametrization. The reported results show that the contribution of the RVS based stellar parameters will be unique in the brighter part of the Gaia survey allowing crucial age estimations, and accurate chemical abundances. This will constitute a unique and precious sample for which many pieces of the Milky Way history puzzle will be available, with unprecedented precision and statistical relevance.
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