We present the studies of nonlinear refraction and nonlinear absorption in promising crystals which are extensively used in Raman lasers or as solid-state laser host materials: Ba(NO3)2, KGW, KYW, and KYbW. The single-beam z-scan technique with 1 ps laser pulses at 790 and 395 nm has been applied for the study. Nonlinear refraction-index intensity-coefficients and two-photon absorption coefficients have been determined for the crystals. The considerable enhancement of nonlinear refraction is observed in the crystals at 395 nm.