We investigate the unsteady motion of mass reservoir formed by the accretion onto the magnetosphere around rotating neutron stars. The unsteady motion of the reservoir induces secondary accretion to neutron star by R-T instability. The nonperiodic or quasiperiodic phenomena of X-ray bursters seems to be related to this property of mass reservoir on the magnetosphere. We classify the typical dynamical state of the reservoir into three types with the parameters which are accretion rate acc and angular velocity of neutron star Ωs. They are nonsequential oscillation, sequential periodic (quasi-periodic) oscillation, and chaotic oscillation states.