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Abstract Electronic excited state is one of the common forms in which atoms, molecules and ions exist in the nature. Study on the characters and dynamics behaviors of the molecular excited states, such as energy levels, lifetimes, predissociation and auto-ionization, as well as on their electronic structures, is not only a significant topic related to chemical reactions and chemical dynamics, but also one of the frontiers in the field of atomic and molecular physics. In present dissertation, experimental studies of the predissociated Rydberg states of CaCl by using the resonance enhanced multiphoton ionization (REMPI) and ion-dip detection spectroscopy were carried out. Five core-penetrating Rydberg states of CaCl in the intermediate effective principle quantum number region, n*=5~7, were observed for the first time. Theoretical analysis confirmed the predissociation mechanism which supposed these Rydberg states were led by an interaction with a 2(+ continuum state. A potential energy curve of this 2(+ continuum state in the energy region of 45000~47500cm-1 was fitted based on the observed predissociation linewidths. Some Rydberg levels with anomalously small rotational constants were also observed. They might be the fragments of the core-nonpenetrating Rydberg states. All these results provide rich information for understanding the mechanism of dissociation of molecules with highly polar core and some correlative dynamical processes. Systematical investigation on the high-lying triplet gerade states of Na2 by using the perturbation facilitated optical-optical double resonance (PFOODR) method is also made. A doubly excited valence state of Na2, 13(g- state, which consists in the unique 3(g- state as well as the unique pure two-electron excitation state below the ionization threshold, was first observed and characterized. A number of v=0~57 vibration levels were determined and assigned. The levels cover more than 99% of the potential well depth of the state. No evid