  Twisted hypercube-like networks (THLNs) are an important class of
interconnection networks for parallel computing systems, which include most
popular variants of the hypercubes, such as crossed cubes, M\"obius cubes,
twisted cubes and locally twisted cubes. This paper deals with the
fault-tolerant hamiltonian connectivity of THLNs under the large fault model.
Let $G$ be an $n$-dimensional THLN and $F \subseteq V(G)\bigcup E(G)$, where $n
\geq 7$ and $|F| \leq 2n - 10$. We prove that for any two nodes $u,v \in V(G -
F)$ satisfying a simple necessary condition on neighbors of $u$ and $v$, there
exists a hamiltonian or near-hamiltonian path between $u$ and $v$ in $G-F$. The
result extends further the fault-tolerant graph embedding capability of THLNs.
