This paper discusses issues, possibilities and existing approaches for fitting an exception handling mechanism (EHM) in CSP-based process-oriented software architectures. After giving a survey on properties desired for a concurrent EHM, specific problems and a few principal ideas for including exception handling facilities in CSP-designs are discussed. As one of the CSP-based frameworks for concurrent software, we extend CT (Communicating Threads) library with the exception handling facilities. The extensions result in two different EHM models whose compliance with the most important demands of concurrent EHMs (handling simultaneous exceptions, the mechanism formalization and efficient implementation) are observed.