Models of the main (core) magnetic field are limited in accuracy by the nature of the data. Anomaly fields from the crust are a noise source in these calculations which restrict the accuracy to which the main field coefficients can be determined. For meaningful coefficients the degree and order of the model is limited to about eight for observatory and other surface data and to about 13 for satellite data. Utilizing satellite and surface data together has permitted the incorporation of a solution for the anomaly field at each observatory. These fields vary from a few tens of nT (nanotesla) to several thousand nT. The residuals of the observatory measurements to such models is no longer dominated by the anomaly fields and so is commensurate with the actual measurement accuracy (about 5 to 20nT, depending on the observatory). Incorporation of the anomaly estimation has made possible the inclusion of stable time derivatives of the spherical harmonic coefficients up to the third derivative. Using these new techniques a spherical harmonic model, designated GSFC (9/80), was derived with degree and order 13 in its constant and first time derivative terms, six in its second time derivative terms, and four in its third derivative terms. The data used in deriving the model included (1) 15, 206 Magsat observations, (2) 71, 000 POGO satellite observations, (3) measurements from 148 magnetic observatories, (4) 300 measurements from filtered marine magnetic data, and (5) approximately 600 measurements from 150 selected repeat stations. The time span of the data was 1960 through 1980. RMS residuals of the model (including anomaly values) to the data are: Magsat scalar data, 10nT; Magsat vector component data, about 7nT; POGO data, 7nT; observatory X component, 38nT; observatory Y component, 19nT; and observatory Z component, 17nT.