In this work, we propose the construction of a two-dimensional system based on the stable phases previously reported for the 2D arsenic and phosphorus compounds, with hexagonal and orthorhombic symmetries. Therefore, we have modeled one hexagonal and three possible orthorhombic structures. To ensure the dynamical stability, we performed phonon spectra calculations for each system. We found that all phases are dynamically stable. To ensure the thermodynamic and mechanical stabilities, we have calculated cohesive energies and elastic constants. Our results show that the criteria for the stabilities are all fulfilled. For these stable structures, we computed the electronic and optical properties from first-principles studies based on density functional theory. The computation of electronic band gaps was performed by using the GW approximation to overcome the underestimation of the results obtained from standard DFT approaches. To study the optical properties, we have computed the dielectric function imaginary part within the BSE approach, which takes into account the excitonic effects and allows us to calculate the exciton binding energies of each system. The study was complemented by the computation of the absorption coefficient. From our calculations, it can be established that the 2D As−P systems are good candidates for several technological applications.