  We conjecture that a 2-connected graph $G$ of order $n$, in which
$d(x)+d(y)\geq n-k$ for every pair of non-adjacent vertices $x$ and $y$,
contains a cycle of length $n-k$ ($k<n/2$), unless $G$ is bipartite and $n-k$
is odd. This generalizes to long cycles a well-known degree sum condition for
hamiltonicity of Ore. The conjecture is shown to hold for $k=1$.
