In high intensity linear accelerators, the tune spreads induced by the space-charge forces in the radial and longitudinal planes are key parameters for halo formation and beam losses. For matched beams they are the parameters governing the number of resonances (including coupling resonances) which affect the beam and determine the respective sizes of the stable and halo areas in phase space. The number and strength of the resonances excited in mismatched beams leading to even higher amplitude halos are also directly linked to the tune spreads. In this paper, the equations making the link between the basic linac parameters (rf frequency, zero-current phase advances, beam intensity and emittances) and the tune spreads are given. A first analysis of the way these linac parameters can be chosen to minimize the tune spreads is presented. The parameters of ESS linac are used for this study.