  We use $K^*_n$ to denote the bidirected complete graph on $n$ vertices. A
nomadic Hamiltonian decomposition of $K^*_n$ is a Hamiltonian decomposition,
with the additional property that ``nomads'' walk along the Hamiltonian cycles
(moving one vertex per time step) without colliding. A nomadic near-Hamiltonian
decomposition is defined similarly, except that the cycles in the decomposition
have length $n-1$, rather than length $n$. J.A. Bondy asked whether these
decompositions of $K^*_n$ exist for all $n$. We show that $K^*_n$ admits a
nomadic near-Hamiltonian decomposition when $n\not\equiv 2\bmod 4$.
