A new data acquisition system designed for a future high-resolution gamma-ray detector array-the Euroball-is described. It will use newly designed high-resolution electronics together with the VXIbus system as the instrumentation bus. The planned electronics and the general structure of the data acquisition system are described in detail. For control and setup of the data acquisition system, Ethernet based communication is planned. The other elements involved in a data acquisition system (readout, graphics, sorting, storage, etc.) are being planned using international standards and a European agreed solution wherever possible. Depending on the possible integration density and the number of channels, the whole system will consist of 10 to 16 VXI crates containing the digitizing electronics and several VME crates for event filter CPUs and data storage control. >