Given a compact
2
2
–dimensional manifold
M
M
we classify all continuous flows
φ
\varphi
without wandering points on
M
M
. This classification is performed by finding finitely many pairwise disjoint open
φ
−
\varphi -
invariant subsets
{
U
1
,
U
2
,
…
,
U
n
}
\{U_1, U_2, \ldots , U_n\}
of
M
M
such that
⋃
i
=
1
n
U
i
¯
=
M
\bigcup _{i=1}^n{\overline {U_i}} = M
and each
U
i
U_i
is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of
φ
\varphi
.