  It has recently been proposed that the accreting collapsed object GRO
J1655--40 could contain a non-zero gravitomagnetic monopole, and hence could be
better described with the more general Kerr-Taub-NUT (KTN) spacetime, instead
of the Kerr spacetime. This makes the KTN spacetime astrophysically relevant.
In this paper, we study properties of various circular orbits in the KTN
spacetime, and find the locations of circular photon orbits (CPOs) and
innermost-stable-circular-orbits (ISCOs). Such orbits are important to
interpret the observed X-ray spectral and timing properties of accreting
collapsed objects, viz., black holes and naked singularities. Here we show that
the usual methods to find the ISCO radius do not work for certain cases in the
KTN spacetime, and we propose alternate ways. For example, the ISCO equation
does not give any positive real radius solution for particular combinations of
Kerr and NUT parameter values for KTN naked singularities. In such a case,
accretion efficiency generally reaches $100\%$ at a particular orbit of radius
$r=r_0$, and hence we choose $r=r_0$ as the `ISCO' for practical purposes.
