Let \(E\) and \(F\) be Borel equivalence relations in Polish spaces. \(E\) is Borel reducible to \(F\), \(E\leq F\), if there is a Borel mapping \(f\) such that \(xEy\Leftrightarrow f(x)Ff(y)\). If \(f\) is a Borel injection, then we say that \(E\) and \(F\) are Borel isomorphic and we write \(E\sqsubseteq F\). We say that \(E\) and \(F\) are Borel bi-reducible, if \(E\leq F\) and \(F\leq E\). Let \(\Delta_X\) be the equality relation on \(X\). If \(|X|= n\), we simply write \(\Delta_n\). \(E\) is smooth, if \(E\leq\Delta_{2^\mathbb{N}}\). A Borel equivalence relation \(E\) is hypersmooth, if \(E =\bigcup_n E_n\), where \(E_0\subseteq E_1\subseteq\dots\) are smooth Borel equivalence relations. Let \(E_0\) and \(E_1\) be the equivalence relations on \(2^\mathbb{N}\) and \((2^\mathbb{N})^\mathbb{N}\), respectively, defined by the same formula: \(xEy\Leftrightarrow \exists n\forall m\geq n\) \((x_m= y_m)\). Both, \(E_0\) and \(E_1\) are hypersmooth and it is well known that \(E_0\leq E_1\), but \(E_1\nleq E_0\). The main result of the paper is the following dichotomy motivated by some results in the measure theoretic context: If \(E\) is a hypersmooth Borel equivalence relation, then either \(E\leq E_0\) or \(E_1\sqsubseteq E\). Let \(E_t\) be the equivalence relation on \(2^\mathbb{N}\) defined by \(xE_ty\Leftrightarrow \exists n\exists k\forall m\) \((x_{n+m}= y_{k+m})\). By R. Dougherty, S. Jackson and A. S. Kechris [Trans. Am. Math. Soc. 341, No. 1, 193-225 (1994; Zbl 0803.28009)] it was proved that up to Borel bi-reducibility \(E_0\) is the unique non-smooth hyperfinite Borel equivalence relation and up to Borel isomorphism \(E_t, E_0\times \Delta_n\), for \(1\leq n\leq \aleph_0\), \(E_0\times\Delta_{2^\mathbb{N}}\) are the unique non-smooth hyperfinite Borel equivalence relations with no finite equivalence classes (let us recall that \((x,y)E\times F(x',y')\Leftrightarrow xEx'\&yFy'\)). In the paper under review some analogs of these results are investigated for hypersmooth Borel equivalence relations. It is proved that up to Borel bi-reducibility \(E_0\) and \(E_1\) are the only two non-smooth hypersmooth Borel equivalence relations and up to Borel isomorphism \(E_0\times (2^\mathbb{N}\times 2^\mathbb{N})\) and \(E_1\) are the only two non-smooth hypersmooth Borel equivalence relations that have equivalence classes of size \(2^{\aleph_0}\). Although the main result involves only notions of classical descriptive set theory, the proof makes heavy use of effective descriptive set theory. On the other hand the proved dichotomy has some global consequences to Borel (not only hypersmooth) equivalence relations. A node is a Borel equivalence relation \(E\) such that for any Borel equivalence relation \(F, E\leq F\) or \(F\leq E\). It follows that the only nodes are \(\Delta_n\), for \(1\leq n\leq \aleph_0\), \(\Delta_{2^\mathbb{N}}\), and \(E_0\). We say that a pair of Borel equivalence relations \((E,E^*)\) with \(E < E^*\) has the dichotomy property, if for any Borel equivalence relation \(F\) either \(F\leq E\) or \(E^*\leq F\). It follows that the only pairs having the dichotomy property are the trivial pairs \((\Delta_n,\Delta_{n+1})\), the pair \((\Delta_{\aleph_0},\Delta_{2^\mathbb{N}})\) (Silver’s theorem), and the pair \((\Delta_{2^\mathbb{N}},E_0)\) (the general Glimm-Effros dichotomy).