Context. The Ge:Ga detectors used in the PACS spectrograph onboard the Herschel space telescope react to changes of the incident flux with a certain delay. This generates transient effects on the resulting signal which can be important and last for up to an hour. Aims: The paper presents a study of the effects of transients on the detected signal and proposes methods to mitigate them especially in the case of the unchopped mode. Methods: Since transients can arise from a variety of causes, we classified them in three main categories: transients caused by sudden variations of the continuum due to the observational mode used; transients caused by cosmic ray impacts on the detectors; transients caused by a continuous smooth variation of the continuum during a wavelength scan. We propose a method to disentangle these effects and treat them separately. In particular, we show that a linear combination of three exponential functions is needed to fit the response variation of the detectors during a transient. An algorithm to detect, fit, and correct transient effects is presented. Results: The solution proposed to correct the signal for the effects of transients substantially improves the quality of the final reduction with respect to the standard methods used for archival reduction in the cases where transient effects are most pronounced. Conclusions: The programs developed to implement the corrections are offered through two new interactive data reduction pipelines in the latest releases of the Herschel Interactive Processing Environment.