The possible existence of the two-dimensional bimagnetoexcitons and metastable bound states formed by two magnetoexcitons with opposite in-plane wave vectors and has been studied. Magnetoexcitons taking part in the formation of molecules look as two electric dipoles with the arms oriented in-plane perpendicular to the respective wave vectors and with the length of the arms where is the magnetic length. Two antiparallel dipoles moving with equal, yet antiparallel, wave vectors have the possibility of moving with equal probability in any direction of the plane, which is determined by the trial wave function of relative motion depending on modulus The magnetoexcitons are composed of electrons and holes situated on the lowest Landau levels with the cyclotron energies greater than the binding energy of the 2D Wannier–Mott exciton. The description has been made in Landau gauge. The spin states of two electrons have been chosen in the form of antisymmetric or symmetric combinations with parameter The effective spins of two heavy holes have been combined in the same resultant spinor states as the spin of the electrons. Because the projections of the both spinor states with are equal to zero, the influence of the Zeeman splitting effect vanishes. In the case of trial wave function , the maximal density of the magnetoexcitons in the momentum space is concentrated on the in-plane ring with radius In the approximation of the lowest Landau levels, when the influence of the excited Landau levels is neglected, stable bound states of bimagnetoexcitons do not exist for both spin orientations. Instead, in the case of and , a deep metastable bound state with the activation barrier comparable with two magnetoexciton ionization potentials has been revealed. In the case of and , only a shallow metastable bound state can appear.