Purification schemes for multiparticle entangled states cannot be trea
ted as straightforward extensions of those two-particle ones because o
f the lack of symmetry they possess. We propose purification protocols
for a wide range of mixed entangled states of many particles. These a
re useful for understanding entanglement, and could be of practical si
gnificance in multiuser cryptographic schemes or distributed quantum c
omputation and communication. We show that operating locally on multip
article entangled states directly is more efficient than relying on tw
o-particle purification.