Spatial and temporal power spectra of the geomagnetic field are useful for stochastic inversion and optimal prediction of the geomagnetic field and its secular variation. Spherical harmonic coefficients for the field and its first time derivative were determined from magnetic observatory annual means and first differences of annual means for each year in the time interval 1910--1983. Internal spherical harmonic coefficients through degree 9 and external zonal coefficients in geomagnetic coordinates for degrees 1, 3, 5, and 7 were included in the analysis. Autocovariance functions for spherical harmonic coefficients of the geomagnetic field were estimated from these coefficients. Characteristic time constants for the estimated internal autocovariance functions depend upon both spherical harmonic degree and whether the autocovariance function is for the field or its first derivative. The characteristic time constant for the field is approximately 10,000 years divided by the square of (n+1/2), where n is the spherical harmonic degree. The characteristic time constant for the first derivative is about a factor of 10 smaller. The first time constant is thought to be related to magnetic diffusion, and the second time constant is thought to be related to core-fluid velocity correlation time. There is also a third time constant of approximately 5 years associated with the second time derivative. External autocovariance functions for degree 1 and degree 3 both show clear evidence of a solar cycle component. A simple analytic expression for the spatial and temporal power spectra of the geomagnetic field was fitted to these data and agrees well with the experimental results. ¿ American Geophysical Union 1996