Disclosed is a method for producing single- or multi-layered fiber preforms by the TFP process with fiber strands which are aligned in particular such that they are oriented with the flux of force, wherein the fiber preforms have virtually any desired material thickness without troublesome backing layers and have virtually any desired surface geometry, comprising the steps of: laying and attaching the fiber strands on a flexible and elastic base, in particular a base formed by an elastomer, with a fixing thread led through a sewing head to form the fiber perform; and lifting the fiber preform off the elastic and flexible base. The fiber preforms produced by means of this method have a virtually optimum fiber alignment, that is to say substantially oriented with the flux of force, and no appreciable flaws in the arrangement of fibers, and consequently make it possible to create composite components that can withstand extreme mechanical stress and are at the same time lightweight, for example by subsequent processing in the RTM process.