A pneumatic valve, includes an air chamber with a supply port to supply compressed air into the air chamber and one or more discharge ports for discharging compressed air from the air chamber. An actuator with a movable closing element and a shape memory alloy SMA element are provided in the valve. The SMA element deforms in response to a supply of electrical heating current and effects an activation of the actuator by movement of the closing element. When the actuator is in an activated state, the closing element blocks the supply of compressed air via the supply port is blocked. When the actuator is in a deactivated state, the closing element enables the supply of compressed air via the supply port. Upon deactivation of the actuator, the closing element is moved by a restoring force into the free setting. The valve includes a check valve with an elastic element.