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The linear accelerators employed to drive Free Electron Lasers (FELs), such as the X-ray Free Electron Laser (XFEL) currently being built in Hamburg, require sophisticated control systems. The Low Level Radio Frequency (LLRF) control system should stabilize the phase and amplitude of the electromagnetic fields in accelerating modules with tolerances below 0.02% for amplitude and 0.01 degree for phase to produce ultra-stable electron beam that meets the conditions required for Self-Amplified Spontaneous Emission (SASE). The LLRF control system of a 32-cavity accelerating module of the XFEL accelerator requires acquisition of more than 100 analogue signals sampled with frequency around 100 MHz. Data processing in a real-time loop should complete within a few hundred nanoseconds. Moreover, the LLRF control system should be reliable, upgradeable and serviceable. The Advanced Telecommunications Computing Architecture (ATCA) standard, developed for telecommunication applications, can fulfil all of these requirements. The paper presents the architecture of a prototype LLRF control system developed for the XFEL accelerator. The control system composed of ATCA carrier boards with Rear Transition Modules (RTM) is able to supervise 32 cavities. The crucial submodules, like DAQ, Vector Modulator or Timing Module, are designed according to the AMC specification. The paper discusses results of the LLRF control system tests that were performed at the FLASH accelerator (DESY, Hamburg) during machine studies.