  This paper grew as a continuation of [Sh462] but in the present form it can
serve as a motivation for it as well. We deal with the same notions, and use
just one simple lemma from there. Originally entangledness was introduced in
order to get narrow Boolean algebras and examples of the nonmultiplicativity of
c.c-ness. These applications became marginal when the hope to extract new such
objects or strong colourings were not materialized, but after the pcf
constructions which made their debut in [Sh:g] it seems that this notion gained
independence. Generally we aim at characterizing the existence strong and weak
entangled orders in cardinal arithmetic terms. In [Sh462] necessary conditions
were shown for strong entangledness which in a previous version was erroneously
proved to be equivalent to plain entangledness. In section 1 we give a forcing
counterexample to this equivalence and in section 2 we get those results for
entangledness (certainly the most interesting case). In section 3 we get weaker
results for positively entangledness, especially when supplemented with the
existence of a separating point. An antipodal case is defined and completely
characterized. Lastly we outline a forcing example showing that these two
subcases of positive entangledness comprise no dichotomy.
