A method for pneumatically conveying material with a pneumatic materials conveying system, such as a waste conveying system, which conveying system comprises: - a main conveying pipe that is connectable as part of a circuit and which comprises at least a first main conveying pipe section and a second main conveying pipe section and a first valve means between the at least two main conveying pipe sections (100A, 100B), wherein the conveying pipe also comprises at least one branch conveying pipe section (80A, 80B), which can be connected to the main conveying pipe section (100A, 100B); - at least one input point of material, more particularly of waste material, connected to a respective one of the at least one branch conveying pipe sections (80A, 80B); - at least two separating devices (90A, 90B), in which the material to be conveyed is separated from the conveying air; - means for producing a pressure difference and/or a conveying air flow in the conveying pipes at least during conveyance of the material, which means for achieving a pressure difference and/or a conveying air flow comprise at least one pump unit, which comprises at least a first pump device and a second pump device; - second valve means (114A, 114B) comprising respective valves (114A, 114B) respectively arranged in the piping between the suction side of each of the at least two pump devices (118A, 118B) and each the at least two separating devices (90A, 90B); - third valve means (110A, 110B) comprising respective three-way valves (110A, 110B) respectively arranged in the piping between the at least two separating devices (90A, 90B) and the main pipe sections (100A, 1008); wherein when the at least one first valve means between the main conveying pipe sections (100A, 100B) is closed, the air flow can be connected simultaneously in the at least two different main conveying pipe sections (100A, 100B) by connecting the suction side of each of the at least two pump devices to a respective main conveying pipe section (100A, 100B) via the respective valve of the second valve means (114A, 114B), the respective one of the at least two separating devices (90A, 90B) and the respective valve of the third valve means (110A, 110B), wherein said at least one input point can be connected to the respective branch conveying pipe section (80A, 80B), material being transferred in a first phase from said input point via said branch conveying pipe section (80A, 80B) into the main conveying pipe section (100A, 100B) by means of the suction/pressure difference and/or the conveying airflow achieved by at least one of the at least two pump devices (118A, 118B), wherein the main conveying pipe section (100A, 100B) is used as a material reservoir, wherein in a second phase the material transferred into the main conveying pipe section is further transferred by means of the suction/pressure difference and/or the conveying air flow achieved by at least one of the at least two pump devices into the at least one of the at least two separating devices (90, 90A, 90B), wherein in said second phase the at least two main conveying pipe sections (100A, 100B) are emptied simultaneously or the material of at least two main conveying pipe sections is transferred into the at least one of the at least two separating devices (90, 90A, 90B) by one main conveying pipe section (100A, 100B) at a time. - a main conveying pipe that is connectable as part of a circuit and which comprises at least a first main conveying pipe section and a second main conveying pipe section and a first valve means between the at least two main conveying pipe sections (100A, 100B), wherein the conveying pipe also comprises at least one branch conveying pipe section (80A, 80B), which can be connected to the main conveying pipe section (100A, 100B); - at least one input point of material, more particularly of waste material, connected to a respective one of the at least one branch conveying pipe sections (80A, 80B); - at least two separating devices (90A, 90B), in which the material to be conveyed is separated from the conveying air; - means for producing a pressure difference and/or a conveying air flow in the conveying pipes at least during conveyance of the material, which means for achieving a pressure difference and/or a conveying air flow comprise at least one pump unit, which comprises at least a first pump device and a second pump device; - second valve means (114A, 114B) comprising respective valves (114A, 114B) respectively arranged in the piping between the suction side of each of the at least two pump devices (118A, 118B) and each the at least two separating devices (90A, 90B); - third valve means (110A, 110B) comprising respective three-way valves (110A, 110B) respectively arranged in the piping between the at least two separating devices (90A, 90B) and the main pipe sections (100A, 1008);