  We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet
gravity and obtain the general form of these solutions in $d$ dimensions. We
find that for all non-extremal NUT solutions of Einstein gravity having no
curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet
gravity that contain these solutions in the limit that the Gauss-Bonnet
parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in
Gauss-Bonnet gravity that yield non-extremal NUT solutions to Einstein gravity
having a curvature singularity at $r=N$ in the limit $% \alpha \to 0$. Indeed,
we have non-extreme NUT solutions in $2+2k$ dimensions with non-trivial
fibration only when the $2k$-dimensional base space is chosen to be
$\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT
solutions whenever the base space is a product of 2-torii with at most a
2-dimensional factor space of positive curvature. Indeed, when the base space
has at most one positively curved two dimensional space as one of its factor
spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though
there a curvature singularity exists at $r=N$. We also find that one can have
bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces
of zero or positive constant curvature. The only case for which one does not
have bolt solutions is in the absence of a cosmological term with zero
curvature base space.
