Up to now, most studies were carried out assuming azimuthally symmetric currents, neglecting the well established longitudinal asymmetry in the geomagnetic disturbance at low- and mid-latitudes during magnetic storms. The asymmetric perturbations superposed upon a symmetric field depression has been attributed by several authors to a a longitudinally limited, partial ring current with field aligned closure through the auroral ionosphere (Cummings; Fukushima and Kamide; and references therein). It has been the objective of the research covered by this report to study the effects of such magnetospheric current systems on the propagation of cosmic ray particles through the domain of the earth's magnetosphere. The corresponding results were expected to demonstrate the significance of cosmic ray measurements as an additional tool for magnetospheric studies, especially in modeling the disturbed magnetic field in the magnetosphere. In this report, first the approach to the problem is reviewed in Section 2, and examples of the basic tools needed in the procedure are illustrated in Section 3. Then, in Section 4, the results of a simple study correlating local perturbations in the geomagnetic field with cosmic ray cutoff rigidity variations are discussed. Section 5 contains a summary of a detailed quantitative analysis on the effects of a partial ring current and of field-aligned currents on both cutoff rigidities and asymptotic directions in different latitude regions. In conclusions, the significance of the results obtained in the entire study is discussed in Section 6 for both magnetospheric and cosmic ray research.