Peculiar velocities superimposed to the Hubble flow distort the mapping between position space and "redshift" space (see figure to the right, a rendering of the galaxy-galaxy correlation function produced by the 2dF Galaxy Redshift Survey Team, 2001). J-PAS's redshift accuracy will be sufficiently good to identify individual not only the galaxies, but the structures themselves (clusters, filaments, walls and voids), both in the angular and in the radial (line-of-sight) directions. Accurate measurements of the redshift-space power spectrum will be possible in the linear and mildly nonlinear regime, and a detailed comparison with theoretical predictions will be done in conjunction with the measurement of BAOs. The measurement of redshift space distortions offer an independent test of the growth history of the peculiar velocity field. This encloses cosmological information on DE (and/or modified gravity) which is complementary to that in BAOs, and which measures the background expansion history. A decomposition of the two-point correlation function in the radial and transverse directions also allows for a measurement of bias b and the amplitude of matter clustering σ8, which can be used to study the growth history of density fluctuations up to z = 1. The measurement of the amplitude of the galaxy power spectrum, P(k), as a function of redshift can also be used to determine the growth rate of structure through the cross-correlation of the galaxy data with future CMB-lensing data, or by using higher-order correlations to determine the bias parameter as a function of scale and redshift. Higher-order correlations, such as the three-point function or bispectrum, will also be used to measure the BAO feature.