High-resolution echelle spectroscopic observations taken with the FEROS spectrograph at the ESO 2.2-m telescope confirm the binary nature of the dMe stars EUVE J0825−16.3 and EUVE J1501−43.6, previously reported by Christian & Mathioudakis (2002). In these binary systems, emission of similar intensity from both components is detected in the Na i D1 & D2, He i D3, Ca II H&K, Ca II IRT and Balmer lines. We have determined precise radial velocities by cross-correlation with radial velocity standard stars, which have allowed us to obtain for the first time the orbital solution of these systems. Both binaries consist of two nearly equal M0V components with an orbital period shorter than 3.5 days. We have analyzed the behaviour of the chromospheric activity indicators (variability and possible flares). In addition, we have determined its rotational velocity and kinematics.