The invention concerns a method for controlling the drive and/or braking power of a locomotive engine at the wheel traction limit, the method calling for the transition to the unstable slip region to be detected by virtue of the increase in wheel speed and the drive or braking power reduced to bring the wheels back into the stable slip region and the drive or braking power subsequently reduced again, etc. In the case of a system operating, with an integrator (13), as a pseudo-dead-axle system, the rpm (frot) of a drive axle is used to calculate an rpm difference (Δn) representing the degree of wheel slip. Using a differentiator (22) to calculate the value of dΔn/dt, the transition to the unstable slip region is determined and, on triggering of a limiting-value stage (43), an additional input parameter acting in opposition to the target value with which it is compared is fed to the integrator (13) until the system returns to the stable slip region. In order to avoid losses in tractive power when traction fails suddenly, the invention proposes that, in addition to the reduction in drive or braking power resulting from calculation of the rpm difference (Δn), a further reduction is made which is dependent on the maximum value reached by the first differential function with respect to time (dΔn/dt) of the difference in rpm (Δn).