- Diagrammatic methods for the calculation of the nonlinear response of a system that is dressed by resonant external fields are developed. The double-sided diagrams used earlier by Prior [IEEE J. Quantum Electron. QE-20, 37 (1984)] for the calculation of nonlinear susceptibilities in the presence of weak fields are generalized. Additional types of double-sided diagrams are given that incorporate explicitly (a) the relaxation-induced population transfers among the dressed levels and (b) the effects of the nonvanishing of the diagonal elements of the dipole operator in the dressed-state basis. The rules for the diagrams are worked out from the analytical structure of the nonlinear response. Applications of the diagrammatic techniques to several intense-field phenomena are discussed. 1992 The American Physical Society.