The phase-coherent recording of pulsar data and subsequent software dispersion removal provide a flexible way to reach the limits of high time resolution, useful for more precise pulse timing and the study of fast signal fluctuations within a pulse. Because of the huge data rate and lack of adequate recording and computing capabilities, this technique has been used mostly only for small pulsar data sets. In recent years, however, the development of very capable, reasonably inexpensive high-speed recording systems and computers has made feasible the notion of pulsar baseband recording and subsequent processing with a workstation/computer. In this paper we discuss the development of a phase-coherent baseband processing system for radio pulsar observations. This system is based on the S2 VLBI recorder developed at ISTS/York University in Toronto, Canada. We present preliminary first results for data from the Vela pulsar, obtained at Parkes, Australia, and processed at ISTS/York University, and discuss plans for future developments.