  We put forward a general classification for a structural description of the
entanglement present in compound entities experimentally violating Bell's
inequalities, making use of a new entanglement scheme that we developed
recently. Our scheme, although different from the traditional one, is
completely compatible with standard quantum theory, and enables quantum
modeling in complex Hilbert space for different types of situations. Namely,
situations where entangled states and product measurements appear ('customary
quantum modeling'), and situations where states and measurements and evolutions
between measurements are entangled ('nonlocal box modeling', 'nonlocal
non-marginal box modeling'). The role played by Tsirelson's bound and marginal
distribution law is emphasized. Specific quantum models are worked out in
detail in complex Hilbert space within this new entanglement scheme.
