Persistent departures from the geocentric axial dipole field model of the time-averaged paleomagnetic field over the past 5 Myr have been analyzed using oceanic data from deep-sea cores and continental data from igneous rocks and sediments. The data set comprises the equivalent of 9490 spot readings of the field (5831 normal and 3659 reverse) from 930 groups of data. Variations in declination anomalies between groups of data strongly suggest the existence of second-order tectonic effects (small rotations) that make it difficult, if not impossible, to identify any nonzonal terms that might exist. Inclination anomalies have therefore been modeled in terms of low-degree zonal harmonics. The calculated inclination anomalies within 10¿ latitude bands are widely scattered (for both oceanic and continental data) and do not appear to have been drawn from distributions with common means. We attribute this large scatter to previously undetected or uncorrected second-order tectonic effects in the continental data or, in the oceanic data, to small departures from the vertical in deep-sea cores. If it is assumed that these effects are random between groups of data and without a systematic bias, they can be averaged out to a large extent if there are sufficient numbers of groups within each latitude band. This method also has the major advantage that it maximizes time averaging of the field. When this is done, an acceptable fit to the inclination anomaly data is found using a zonal harmonic model. Although the point estimates for the reverse polarity zonal quadrupole term are consistently larger than those for the normal polarity zonal quadrupole term, the difference is not significant and is likely due to contamination effects. This finding is true for a combination of all the data or for separate combinations of continental igneous rocks and ocean sediments. This conclusion differs from all previous analyses. The major differences occur in model estimates of the zonal octupole term, the estimates varying widely depending on the particular data combination. We show that false octupole terms can be introduced by several factors, including inclination errors in sediments and lavas, the use of unit vectors in the analyses, and incomplete magnetic cleaning, particularly of reversely magnetized rocks. Thus we cannot impute a geomagnetic significance to the estimates of a zonal octupole term. We suggest that the best estimates for the zonal quadrupole G2=g02/g01 are obtained from the combined Brunhes age igneous rocks and oceanic normal data (0.033¿0.019) and for the combined Matuyama age igneous rocks and oceanic reverse data (0.042¿0.022). When these two sets are combined, the overall best estimate of G2 is 0.038¿0.012. ¿ American Geophysical Union 1996