Approximation numbers of the embedding operator of the nonisotropic Sobolev space W(m), 2(Q) into L2(Q), Q being an n-dimensional open box, are applied to the study of spectral asymptotics. We deal with the nonisotropic polyharmonic operators on bounded and quasibounded open sets in Rn. The quasibounded open sets are required to satisfy theG k,a (m),2 -condition. Not only the leading terms of the asymptotic formulae but also remainder terms are obtained. An application is made to a quasibounded domain whose width has a negative power-type decay at infinity.