  We propose two schemes for concentration of hyperentanglement of nonlocal
multipartite states which are simultaneously entangled in the polarization and
spatial modes. One scheme uses an auxiliary singlephoton state prepared
according to the parameters of the less-entangled states. The other scheme uses
two less-entangled states with unknown parameters to distill the maximal
hyperentanglement. The procrustean concentration is realized by two parity
check measurements in both the two degrees of freedom. Nondestructive quantum
nondemolition detectors based on cross-Kerr nonlinearity are used to implement
the parity check, which makes the unsuccessful instances reusable in the next
concentration round. The success probabilities in both schemes can be made to
approach unity by iteration. Moreover, in both schemes only one of the N
parties has to perform the parity check measurements. Our schemes are efficient
and useful for quantum information processing involving hyperentanglement.
