  By a gradient-like flow on a closed orientable surface $M$, we mean a closed
1-form $\beta$ defined on $M$ punctured at a finite set of points (sources and
sinks of $\beta$) such that there exists a Morse function $f$ on $M$, called an
energy function of $\beta$, whose critical points coincide with equilibria of
$\beta$, and the pair $(f,\beta)$ has a canonical form near each critical point
of $f$. Let $\mathcal{B}=\mathcal{B}(\beta_0)$ be the space of all
gradient-like flows on $M$ having the same types of local singularities as a
flow $\beta_0$, and $\mathcal{F}=\mathcal{F}(f_0)$ the space of all Morse
functions on $M$ having the same types of local singularities as an energy
function $f_0$ of $\beta_0$. We prove that the spaces $\mathcal{F}$ and
$\mathcal{B}$, equipped with $C^\infty$ topologies, are homotopy equivalent to
some manifold $\mathcal{M}_s$, moreover their decompositions into
$\mathrm{Diff}^0(M)$-orbits are given by two transversal fibrations on
$\mathcal{M}_s$. Similar results are proved for topological equivalence classes
on $\mathcal{F}$ and $\mathcal{B}$, and for non-Morse singularities.
