To any continuum X we assign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application we construct an uncountable family of metric continua X homeomorphic to C(X).Introduction. The idea of using ordinal numbers as a "measure" of some local or global properties of (compact) spaces is not new. Usually these properties are related to (non-)connectedness, and the defined "measure" can be used as a tool in studying various other properties of investigated spaces, both structural (internal) and mapping (external) ones. For example, Iliadis in [14] defines the notion of a normal sequence for hereditarily decomposable and hereditarily unicoherent metric continua (i.e., for λ-dendroids) as follows. Let X be such a continuum. A continuum H ⊂ X is said to be in I(X) if, given any decomposition of X into finitely many subcontinua, H is contained in one element of the decomposition. Let Σ = {H α : α < λ} be a transfinite sequence of subcontinua of X, where λ is some countable ordinal number. Then Σ is called a normal sequence if (i) H 0 = X, (ii) H β = I(H α ) for ordinals β = α + 1, (iii) H β = ∩{H α : α < β} for limit ordinals β, and (iv) for each α < λ the continuum H α is nondegenerate. The least upper bound (or minimum) k(X) of the lengths of all normal sequences in X is called the depth of X. The concept was used to study various phenomena in λ-dendroids. For its modification, see [31].