A new data acquisition system, ToF-DAQ, has been developed for a ToF-ERDA telescope and other ToF-E and ToF-ToF measurement systems. ToF-DAQ combines an analogue electronics front-end to asynchronous time stamped data acquisition by means of a FPGA device. Coincidences are sought solely in software based on the timestamps. Timestamping offers more options for data analysis as coincidence events can be built also in offline analysis. The system utilises a National Instruments R-series FPGA device and a Windows PC as a host computer. Both the FPGA code and the host software were developed using the National Instruments LabVIEW graphical programming environment. Up to eight NIM ADCs can be handled by a single FPGA. The host computer and the FPGA can process total continuous count rates of over 750000 counts/s with a timestamping resolution of 8.33 ns.