The compression of LANDSAT images using Hilbert or Peano scanning and adaptive arithmetic coding is considered. The Hilbert scan is a general technique for continuous scanning of multidimensional data. Arithmetic coding has established itself as the superior method for lossless compression. This paper extends on previous work on the integration of the arithmetic coding methodology and an n-dimensional Hilbert scanning algorithm developed by Perez, Kamata and Kawaguchi. Hilbert scanning preserves the spatial continuity of an image, on both the x and y directions, and a higher correlation exists between continuous points than in a raster scan. Therefore, a Hilbert adaptive scheme can better estimate the local probability distributions. Arithmetic coding is most efficient when the probabilities of the symbols are close to one. Therefore, by integrating both the spatial and spectral information into a unified context a high rate of compression can be achieved.