We present a response theory formulation for the dependence of nuclear magnetic shielding on the external magnetic field B-0 in closed-shell atomic systems. The dependence appears in even powers of B-0, and we include terms up to the sixth power of the field. Calculations are carried out for the field-dependence coefficient tau for noble gas atoms as well as halogen and alkali metal ions, based on a nonrelativistic reference state, using self-consistent field (SCF) and correlated multiconfigurational SCF linear and nonlinear response methods. (C) 2003 Elsevier Science B.V. All rights reserved.