We consider a model of strongly correlated e_g electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO₃. It is found that the classical orbital order with alternating occupied e_g orbitals has a full rotational symmetry at orbital degeneracy, and the excitation spectrum derived using the linear spin-wave theory is gapless. The quantum corrections to the order parameter and to the ground state energy restore the cubic symmetry of the model. By applying a uniaxial pressure orbital degeneracy is lifted in a tetragonal field and one finds an orbital-flop phase with a gap in the excitation spectrum. In two dimensions the classical order is more robust near the orbital degeneracy and quantum effects are suppressed. The orbital excitations obtained using finite temperature diagonalization of two-dimensional clusters consist of a quasiparticle accompanied by satellite structures. The orbital waves found within the linear spin-wave theory provide an excellent description of the dominant pole of these spectra.