New types of spintronics devices utilizing all-electrical magnetization manipulation by current, such as spin-torque transfer RAM and spin-torque oscillators, have been developed based on MgO magnetic tunnel junctions (MTJs) . Spin-torque oscillators based on MTJs with in-plane magnetization  show high frequency capabilities, but still need an external magnetic field and are characterized by a low output power level . Oscillators based on MTJs with perpendicular magnetization  and vortex-based oscillators  are shown to generate oscillations without external magnetic field, however, their operating frequencies are low, usually below 2GHz . In this work we investigate by means of extensive micromagnetic simulations bias-field-free nano-oscillators based on two MgO-MTJs with a shared free layer with in-plane magnetization. First we investigated a penta-layer MTJ structure with only half-elliptic pinned layers (Fig.1). Fig.2 shows the switching process in such a structure in detail. We find that the structure with half-ellipsis pinned layers develops stable oscillations with nearly constant amplitude. The Fourier transform of the signal is sharply peaked around the frequency ~6.785GHz (Fig.3, top). We note that the frequency of the oscillations only slightly depends on the current value (Fig. 3, bottom). However, a problem is that despite the partial coverage of the free layer by the fixed layers, resulting in spin-current injection in only a part of the free layer (Fig.4, inset), the free layer magnetization switching still occurs at a wide range of current densities (Fig.4). The magnetization dynamics of the free layer at different instances during the switching process is shown in Fig.5. In order to prevent the switching of the free layer, thus improving an oscillatory behavior control, we have added the second MgO-MTJ to the system (Fig.6). Fig.7 shows the switching process in such a structure in detail. We find that, in contrast to the previously considered case, the structure with two MgO-MTJs demonstrates stable oscillations with a constant amplitude. The Fourier transform of the signal is sharply peaked around the frequency of 13GHz (Fig.8). The proposed structure can be used to fabricate bias-field-free nano-oscillators.