In this paper the error probability of a singlechannel coherent optical DPSK transmission system based on repeterless links in the presence of fiber chromatic dispersion and Kerr effect is evaluated. An accurate model for both the optical signal propagation and the probability distribution of the receiver decision variable is adopted by using a numerical solution of the non-linear Shrodinger equation and the characteristic function method. The obtained results show that the selection of an optimized IF filter bandwidth is crucial in order to obtain the best system performance. When chromatic dispersion dominates its combination with Kerr effect causes best performances to be achieved in normal dispersion region while, when Kerr effect is the most relevant limitation factor for the system performances, the lowest error probability is attained in anomalous regime. As a matter of fact in this regime Kerr effect and chromatic dispersion tends to partially compensate each other. In any case the error probability curves shows a relative minimum that is always attained in the anomalous region. Finally the maximum link length is limited by the presence of Kerr effect independently from the amount of transmitted optical power to be shorter than a threshold length if an error probability of is to be achieved.