The possible existence of bound states of the interacting two-dimensional (2D) magnetoexcitons with different spin structures in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. The magnetoexcitons taking part in the formation of the bound state with resultant wave vector 0 k = have opposite in-plane wave vectors k and k - and look as two electric dipoles with the arms oriented in-plane perpendicularly to the corresponding wave vectors. The length of the arms equals to 2 0 , d kl = where 0l is the magnetic length. The bound state of two antiparallel dipoles moving with equal but antiparallel wave vectors in any direction of the plane with equal probability is characterized by the variational wave function of the relative motion ( ) n j k depending on the modulus | k | . The magnetoexcitons are composed of electrons and holes situated on the LLLs with cyclotron energies greater than the binding energies of the 2D Wannier-Mott exciton, and interact through the Coulomb interactions of their constituents. The spins of the electrons and the effective spins of two holes forming the bound states were combining separately in the symmetric or in the antisymmetric forms ( ­¯ +h ¯­ ) with the same parameter h = ±1 for electrons and holes. Two types of wave functions, one with singlet electron and singlet hole structure and another one with triplet electron and triplet hole structure were used, leading to completely different bound states. The mixt states of the type singlet electrons and triplet hole or vice versa do not exist due to the hidden symmetry of the electron and hole in the lowest Landau levels in the Landau gauge description. Because the projections of the both spinor states with h = ±1 are equal to zero, the effect of the Zeeman splitting vanishes.The para and ortho magnetoexciton states up till now were not investigated and the splitting of their energy levels is unknown at present time. In the case of the variational wave function 2 2 3 1 2 2 2 0 2 0 ( ) (8 ) k l k k l e a j a - = the maximum density of the magnetoexcitons in the momentum space representation is concentrated on the in-plane ring with the radius 0 1 ( ). r kla = In the LLLs approximation, when the influence of the excited Landau levels (ELLs), as well as of the Rashba spin-orbit coupling (RSOC) are neglected, the stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations. Instead of them, a deep metastable bound state with the activation barrier comparable with double ionization potentials 2 l I of the magnetoexciton with 0 k = was revealed in the case 1h= and 0.5 a = . In the case 1h=- and 3.4 a = only a shallow metastable bound state can appear. In the case of the variational wave function 2 2 1 2 0 0 ( ) (4 ) k l k ea j a - = all the bound states are unstable and the molecule bimagnetoexciton cannot be formed in the LLLs approximation.