In this paper, we address the problem of lossless and nearly- lossless multispectral compression of remote-sensing data acquired using SPOT satellites. Lossless compression algorithms classically have two stages: Transformation of the available data, and coding. The purpose of the first stage is to express the data as uncorrelated data in an optimal way. In the second stage, coding is performed by means of an arithmetic coder. In this paper, we discuss two well-known approaches for spatial as well as multispectral compression of SPOT images: (1) The efficiency of several predictive techniques (MAP, CALIC, 3D predictors), are compared, and the advantages of 2D versus 3D error feedback and context modeling are examinated; (2) The use of wavelet transforms for lossless multispectral compression are discussed. Then, applications of the above mentioned methods for quincunx sampling are evaluated. Lastly, some results, on how predictive and wavelet techniques behave when nearly-lossless compression is needed, are given.