Hydraulic braking device for a crane drive and crane

The apparatus has a hydraulic stopping brake designed as a spring-applied multi-disk brake (50) for braking drive movement of a crane drive in an emergency situation. A directly controlled pressure regulation valve (70) controls the brake to ensure time-delayed braking torque build-up. A control pressure line (80) of the regulation valve is coupled to a supply pressure line (81) of the brake via a ski selector valve (90). A pressure storing unit is provided in the supply pressure line of the brake to compensate total pressure drop.