Abstract: This paper studied some problems of multivariate geostatistics which involve four parts: 1, Bas;c hypothesis of multivariate geostatistics, include coregionalized variable, cross-variogram, cross-covariance, the statio-narity of order 2 and the intrinsic hypothesis of coregionalized variables; 2, coregionalization matrices; 3, Linear model of coregionalization; 4, The best estima ted methods for multivariate geostatistics include estimation of the regionalized variables with cokriging, estimation of the spatial components and estimation of the regionalized factors.