Based on an independent-particle-approximation (i.e. the multiplescattering self-consistent-field theory), we studied the electronic structures of Rydberg states of the small diatomic molecules H2, He2 and the He2+ molecular ion. The principal quantum number of the first state of the Rydberg series is determined from a convention of the limit of the molecular electronic configuration. The dynamics of the excited molecules and molecular ion has been elucidated. Our theoretical results are in fair agreement with the existing experimental measurements, thus they can serve as a reliable basis for future refined treatment such as the configuration interaction calculation.