Continuous wavelet transform (CWF) analysis reveals the instantaneous variability of foraminiferal delta (super 18) O and delta (super 13) C at ODP Site 1143 for the past 5 Ma at the eccentricity, obliquity and precession bands. Cross CWT analysis further demonstrates the nonstationary phases of benthic delta (super 18) O relative to ETP at the three primary Milankovitch bands in the last 5 Ma. The instantaneous phases between benthic delta (super 18) O and delta (super 13) C at the precession band display a prominent 128 ka period, probably the cyclicity of the nonstationary climate close to the eccentricity. To explain these nonstationary phases, it is desirable to introduce a nonlinear response model to the global climate system, in which the output has a prominent cycle around 100 ka to match the 128 ka cycle of the instantaneous phase of delta (super 13) C and delta (super 18) O on the precession band.