NMR cross-polarization (CP) measurements are usually analyzed assuming that the cross-polarization time T-IS of magnetization transfer from the abundant I spins to the rare S spins is shorter than the relaxation time T-1 rho in the rotating frame of the I spins (fast CP regime). Here, it is shown that the reverse situation (T-IS > T(1)rho (I), slow CP regime) may occur, for instance, for the H-1-->Si-29 transfer in commonly encountered inorganic materials and that analyzing the experimental data in this case under the usual fast CP assumption will, beside leading to erroneous dynamic parameters, underestimate the number of spins by a factor similar toT(IS)/T-1 rho,. Experimental ways to distinguish between the two situations are presented, the most efficient being to resort to the TORQUE experiment. Examples are given on silica gel and calcium silicate hydrate (CSH)samples for which the proper analysis allows a deeper insight into the nature of the protonated surfaces. This slow CP regime may be expected to occur also in some organic materials, for instance in C-13 NMR of polyaromatic compounds.