A longitudinal dynamics management device for vehicles is provided, the device having at least one first function unit which performs predetermined driving functions by output of a longitudinal dynamics management setpoint value, and a second function unit which is independent of the first function unit. The safety functions of the second function unit are performed independently of internal operands of the first function unit. The safety functions include acceleration monitoring and/or monitoring of jolts. With acceleration monitoring, a check is performed to ascertain whether the actual vehicle acceleration and/or the expected acceleration resulting from the setpoint value is independent of a setpoint vehicle acceleration, within an acceleration range regarded as controllable by the driver. With jolt monitoring, a check is performed to ascertain whether the change in actual vehicle acceleration and/or the expected change in vehicle acceleration is within a range regarded as controllable by the driver.