  We study the spectroscopic binary system Gl 375. 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. 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 M_sun and
M_2 sin^3 i =0.33 M_sun) 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 synchronized 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. 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 approximately 2.2 years (800 days) is
consistent with previous determinations of activity cycles in similar stars.
