The governing equations are derived for the analysis of a stepped labyrinth gas seal generally used in high performance compressors, gas turbines, and steam turbines. The bulk-flow is assumed for a single cavity control volume set up in a stepped labyrinth cavity and the flow is assumed to be completely turbulent in the circumferential direction. The Moodys wall-friction-factor model is used for the calculation of wall shear stresses in the single cavity control volume. For the reaction force developed by the stepped labyrinth gas seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about a centered position. Integration of the resultant first-order pressure distribution along and around the seal defines the rotordynamic coefficients of the stepped labyrinth gas seal. The resulting leakage and rotordynamic characteristics of the stepped labyrinth gas seal are presented and compared with Scharrers theoretical analysis using Blasius wall-friction-factor model. The present analysis shows a good qualitative agreement of leakage characteristics with Scharrers analysis, but underpredicts by about 20%. For the rotordynamic coefficients, the present analysis generally yields smaller predictied values compared with Scharrers analysis.