Linear motor-driven conveying system, in particular stretching and simultaneous stretching system, having the following features: - having a guide rail and/or conveying rail (15; 115, 117) along which a gripperconveying unit having a gripper part and a conveying part is displaceable lengthways by a linear motor drive, - the linear motor drive comprises secondary parts which are displaceable with the conveying part, are attached fixedly thereto and are preferably in the form of permanent magnets, and comprises fixed primary parts in a small spacing gap (Sp) therefrom, for generating electromagnetic fields, the primary parts acting on a motor engagement side of the secondary parts while the secondary parts continue to move, - the gripper part comprises a clamping device for fixing an edge of a material web, thereby defining a material web plane, characterised by the following further features: - the conveying system comprises either a) only one linear motor drive provided below the conveying part, or b) only one linear motor drive provided above the conveying part, or c) one linear motor drive arranged below and one arranged above the conveying part, the upper linear motor drive and/or the associated control means being configured such that the upper linear motor drive is operable only at a maximum power of 75 % with respect to the maximum power of the lower linear motor drive, - the conveyed web can be fixed to the gripper part, thereby defining a conveyed web plane, this film plane being arranged at a height distance with respect to the motor engagement side of the single linear motor drive or of the more powerful linear motor drive in the case of two linear motor drives, and this height distance being less than or equal to the length of the secondary parts on the conveying parts. - having a guide rail and/or conveying rail (15; 115, 117) along which a gripperconveying unit having a gripper part and a conveying part is displaceable lengthways by a linear motor drive, - the linear motor drive comprises secondary parts which are displaceable with the conveying part, are attached fixedly thereto and are preferably in the form of permanent magnets, and comprises fixed primary parts in a small spacing gap (Sp) therefrom, for generating electromagnetic fields, the primary parts acting on a motor engagement side of the secondary parts while the secondary parts continue to move, - the gripper part comprises a clamping device for fixing an edge of a material web, thereby defining a material web plane, - the conveying system comprises either a) only one linear motor drive provided below the conveying part, or b) only one linear motor drive provided above the conveying part, or c) one linear motor drive arranged below and one arranged above the conveying part, the upper linear motor drive and/or the associated control means being configured such that the upper linear motor drive is operable only at a maximum power of 75 % with respect to the maximum power of the lower linear motor drive, a) only one linear motor drive provided below the conveying part, or b) only one linear motor drive provided above the conveying part, or c) one linear motor drive arranged below and one arranged above the conveying part, the upper linear motor drive and/or the associated control means being configured such that the upper linear motor drive is operable - the conveyed web can be fixed to the gripper part, thereby defining a conveyed web plane, this film plane being arranged at a height distance with respect to the motor engagement side of the single linear motor drive or of the more powerful linear motor drive in the case of two linear motor drives, and this height distance being less than or equal to the length of the secondary parts on the conveying parts.