We present optimal measuring strategies for an estimation of the entangleme
nt of unknown two-qubit pure states and of the degree of mixing of unknown
single-qubit mixed states, of which N identical copies are available. The m
ost general measuring strategies are considered in both situations, to conc
lude in the first case that a local, although collective, measurement suffi
ces to estimate entanglement, a nonlocal property, optimally.