The nonstationary behavior of a cracked rotating shaft with a disk is analyzed. The shaft is accelerated or decelerated through a critical speed, and both flexural and torsional responses are examined. A breathing crack is considered, which is either completely open or completely closed at any given time. Forces due to eccentricity, gravity, and internal and external damping are included. Galerkin’s method is utilized, and the resulting bilinear equations are integrated numerically. The effects of acceleration and deceleration rate, internal and external damping, crack location and depth, and location, mass, and eccentricity of the disk are investigated. Application of the results to detection of cracks is discussed.