To constrain theories for the dynamic evolution of global ice mass through the late Neogene, it is important to determine whether major changes in the record were gradual or rapid. Of particular interest is the evolution of the near 100‐kyr ice age cycle in the middle Pleistocene. We describe and apply a new technique based on multiple taper spectral analysis which allows us to model the time evolution of quasi‐periodic signals. This technique uses both phase and amplitude information and enables us to address the question of abrupt versus gradual onset of the 100‐kyr periodicity in the middle Pleistocene. We analyzed three long (>2.6 m.y.) time series from Deep Sea Drilling Project (DSDP) site 607 (midlatitude Atlantic) and Ocean Drilling Program (ODP) site 677 (equatorial Pacific). The published time scales for these sites differ significantly, influencing the interpretation of the mid‐Pleistocene climate transition. When the data series are expressed on the same time scale, there is evidence for a coherent δ18O signal at both sites in the eccentricity and obliquity frequency bands, consistent with variations in global ice volume as the causative factor. If the Shaddeton et al. (1990) time scale for ODP 677 is accepted, the amplitude match between the δ18O obliquity cycle and the 65°N insolation derived from the recent astronomical solution of Laskar (1988, 1990) is excellent for timest≲2.3 Ma. If the Ruddiman/Raymo time scale for DSDP 607 is accepted, the 41‐kyr δ18O cycle has enhanced amplitude between 1.0 and 1.5 Ma, relative to the late Pleistocene (t<1.0 Ma), implying a nonlinear Earth system response to obliquity insolation cycles. We do not find compelling evidence for an abrupt change in the 100‐kyr δ18O signal, although we cannot rule it out at this time. If the Shackleton et al. (1990) time scale for ODP 677 is accepted, our three δ18O records are consistent with a low‐amplitude 100‐kyr cycle between 1.2 and 2.6 Ma, whose local period of oscillation alternates between the 95‐ and 124‐kyr eccentricity periods, and a gradual increase in the 100‐kyr δ18O signal between 0.5 amd 1.0 Ma. The DSDP 607 time scale is more favorable to an abrupt jump in amplitude for the 95‐kyr δ18O envelope, but not in the 124‐kyr envelope. Rather, long‐period δ18O fluctuations appear phase‐locked with the 124‐kyr eccentricity cycle some 300–400 kyr prior to its growth in amplitude and phase‐lock with the 95