  Let $f:T^2\to\mathbb{R}$ be a Morse function on $2$-torus $T^2$ such that its
Kronrod-Reeb graph $\Gamma(f)$ has exactly one cycle, i.e. it is homotopy
equivalent to $S^1$. Under some additional conditions we describe a homotopy
type of the orbit of $f$ with respect to the action of the group of
diffeomorphism of $T^2$.
  This result holds for a larger class of smooth functions $f:T^2\to\mathbb{R}$
having the following property: for every critical point $z$ of $f$ the germ of
$f$ at $z$ is smoothly equivalent to a homogeneous polynomial
$\mathbb{R}^2\to\mathbb{R}$ without multiple factors.
