Four methods for nuclear polarization and alignment are discussed and compared. In particular, a general theorem regarding the leading term in the expression for nuclear polarization by hfs coupling with external field is obtained. A general method is derived for treating the computation of higher order terms in the expansions of these quantities, as well for use with complicated hamiltonians, and application is made to three cases of interest. It is shown that the higher order terms are very small, in cases of interest, compared to the leading terms.