A procedure is presented for estimating the changes in the cosmic ray cutoff rigidity and the asymptotic directions during geomagnetically active time periods at low- and mid-latitude locations. At a specific location the change in the rigidity associated with the first discontinuity in asymptotic longitude, ΔR1, and the equivalent changes in the other cutoff rigidity parameters can be related to the weighted sum of the changes in the horizontal component of the equatorial surface magnetic field, ΔHeq, sampled at intervals of 1 hour in local time from 0000 to 0700 to the east of the specified location. A set of generalized weighting factors is given for eight cutoff rigidity values in the range from 3 to 13.5 GV. For a cosmic ray particle having a rigidity R the asymptotic direction of approach during perturbed conditions corresponds in good approximation to the asymptotic direction of a particle with rigidity R -ΔR1 propagating through the quiescent geomagnetic field. Asymptotic directions during geomagentically active periods can therefore be derived from the asymptotic directions computed in a quiescent geomagnetic field model after the associated change in the cutoff rigidity has been deducted from ground-based magnetometer data. The basic principles of the procedure are demonstrated for the cosmic ray station Jungfraujoch, Switzerland.