A machine for filling and closing containers comprises: a conveyor, step-activated in an advancement direction, laterally provided with a plurality of gripping devices which grip containers at an active branch of the conveyor. A filling station has a plurality of nozzles for filling the containers, and weighing devices for detecting a correct filling of the containers. A closing station has capping devices for closing the filled containers with caps, and sensors to detect correct closure. A release station, located downstream of the closing station has manipulators which are either de-activated to allow transit of incorrectly filled and/or closed containers, which are released onto a reject conveyor downstream and in line with the active branch; or activated transversally to the advancement direction to collect correctly filled and closed containers and release them onto an outlet conveyor, adjacent and parallel to the reject conveyor.