The molecular dynamics of nuclear protein import were examined in a solution binding assay by testing for interactions between a protein containing a nuclear localization signal (NLS), the transport factors karyopherin alpha, karyopherin beta, and Ran, and FXFG or GLFG repeat regions of nucleoporins. We found that karyopherins alpha and beta cooperate to bind FXFG but not GLFG repeat regions. Binding of the NLS protein to karyopherin alpha was enhanced by karyopherin beta. Two novel reactions were discovered. First, incubation of a karyopherin heterodimer-NLS protein complex with an FXFG repeat region stimulated the dissociation of the NLS protein from the karyopherin heterodimer. Second, incubation of the karyopherin heterodimer with RanGTP (or with a Ran mutant that cannot hydrolyze GTP) led to the dissociation of karyopherin alpha from beta and to an association of Ran with karyopherin beta; RanGDP had no effect. We propose that movement of NLS proteins across the nuclear pore complex is a stochastic process that operates via repeated association-dissociation reactions.