The Boltzmann equation deals with a distributionf(x, ), wherex denotes the space variable and is the momentum. The hydrodynamic equations deal with-moments of the distribution. The paper deals with the derivation of the hydrodynamic equations in the case that the collision kernel is Maxwellian, i.e., independent of the velocity. For such a kernel, a computational tool, based on the theory of representations of the orthogonal group, is developed. With this tool it is possible to derive systems of equations for any number of moments. The construction of closed systems is based on asymptotic estimates for solutions of Boltzmann equations. These show that, in some definite sense, an approximating system involving moments of high order is more accurate than a system of lower order.