Using first order classical perturbation theory, we generalize the closed orbit theory from atime-independent system to a time-dependent one and calculate the recurrencespectra of a Li Rydberg atom in a static magnetic plus an oscillating electric field.The results show that when the oscillating field was added, the strength of therecurrence spectra was greatly decreased. The recurrence spectra whose periodsare integer multiples or near-integer multiples of the period of the perturbatingoscillating field survive, while those that are not integer multiples of the periodof the oscillating field are weakened or vanish. As the scaled electric fieldf increases,the peaks of the recurrence spectra lose strength. Some recurrences are dropped rapidly and disappear asf increases; others existeven at much higher f.The results in this paper are very useful for future experimental research.