A recently proposed spin-restricted open-shell Kohn-Sham (ROKS) method is applied to investigate various atomic and molecular multiplet states. A wide range of multiplets is considered: multiplet terms for which the spin-restricted open-shell theory of Roothaan applies, as well as state situations which cannot be described by Roothaan＇s theory (e.g., states of square cyclobutadiene, etc.). Problems associated with the use of approximate density functionals and possible perspectives of the ROKS method are discussed.