The main aim of this paper is to show the utility of cokriging for image fusion (i.e. increasing the spatial resolution of satellite sensor images). It is assumed that co-registered images with different spatial and spectral resolutions of the same scene are available and the task is to generate new remote sensing images at the finer spatial resolution for the spectral bands available only at the coarser spatial resolution. The main advantages of cokriging are that it takes into account the correlation and cross-correlation of images, it accounts for the different supports (i.e. pixel sizes), it can take into account explicitly the point spread function of the sensor and has the property of prediction coherence. In addition, ancillary images (topographic maps, thematic maps, etc.) as well as sparse experimental data could be included in the process. The main drawback of cokriging in the previous context is that it requires several covariances and cross-covariances some of which are not accessible empirically (i.e. from the pixel values of the images). The solution adopted in this paper was to use linear systems theory to obtain the required covariances from the ones that were estimated empirically. Cokriging was compared with a benchmark image fusion approach (the high pass filter method) to assess performance against a standard. In fact, cokriging may be seen as a generalization of the high pass filter method where the low pass filter and high pass filter are estimated by fitting parameters to data. The present paper discusses the downscaling cokriging method, shows its implementation and illustrates the process in the case of sharpening several remotely sensed images. The desired target image was known so that the performance of the method could be evaluated realistically. Different statistics were used to show that the cokriged predictions were more precise than the HPF predictions. Downscaling cokriging is a new method of great potential in remote sensing that should be incorporated to the toolkit of the remote sensing researcher.