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At GSI, Darmstadt, Germany, a Barrier-Bucket (BB) RF System is currently under development for the Experimental Storage Ring (ESR). The system consists of two broadband RF cavities, each driven by a solid state amplifier, with the purpose to produce two voltage pulses per beam revolution. This will enable highly sophisticated longitudinal beam manipulations like longitudinal capture, compression and decompression or stacking of the beam. For the LLRF System, several requirements have to be fulfilled. Besides high standards concerning the pulsed gap signal quality (e.g. ringing < 2.5%), the system has to provide the flexibility for adiabatic voltage ramp-up and adiabatic pulse shifting with high timing accuracy. A connection to the FAIR Central Control System (CCS) is necessary, as amplitude and phase ramp data will be provided by the CCS. In this contribution, the structure of the ESR BB LLRF system is presented together with experimental results from the first setup of the system.