This invention is directed generally to substituted pyridinone and pyrimidinone compounds that generally inhibit p38 kinase, TNF, and/or cyclooxygeπase activity. Such substituted pyridinone and pyrimidinone compounds include compounds generally corresponding in structure to the following formula: wherein Z, n, R1, R2a, R2b, R2c, R2d, R2e, R3a, R3b, R3c, R3d, R4, R5, R6, R7a, R7b, R7c, R7d and R7e are as defined in this specification. This invention also is directed to compositions of such substituted pyridinones and pyrimidinones (particularly pharmaceutical compositions), and methods for treating disorders (typically pathological disorders) associated with p38 kinase activity, TNF activity, and/or cyclooxygenase-2 activity.