Context :

Aims : We study the spectroscopic binary system Gl 375 .

Methods : We employ medium resolution echelle spectra obtained at the 2.15 m telescope at the Argentinian observatory CASLEO and photometric observations obtained from the ASAS database .

Results : We separate the composite spectra into those corresponding to both components .
The separated spectra allow us to confirm that the spectral types of both components are similar ( dMe3.5 ) and to obtain precise measurements of the orbital period ( P = 1.87844 days ) , minimum masses ( M _ { 1 } \sin ^ { 3 } i = 0.35 \mathrm { M } _ { \odot } and M _ { 2 } \sin ^ { 3 } i = 0.33 \mathrm { M } _ { \odot } ) and other orbital parameters .
The photometric observations exhibit a sinusoidal variation with the same period as the orbital period .
We interpret this as signs of active regions carried along with rotation in a tidally synchronised system , and study the evolution of the amplitude of the modulation in longer timescales .
Together with the mean magnitude , the modulation exhibits a roughly cyclic variation with a period of around 800 days .
This periodicity is also found in the flux of the Ca II K lines of both components , which seem to be in phase .

Conclusions : The periodic changes in the three observables are interpreted as a sign of a stellar activity cycle .
Both components appear to be in phase , which implies that they are magnetically connected .
The measured cycle of \approx 2.2 years ( \approx 800 days ) is consistent with previous determinations of activity cycles in similar stars .