  A graph is called pseudo-outerplanar if each block has an embedding on the
plane in such a way that the vertices lie on a fixed circle and the edges lie
inside the disk of this circle with each of them crossing at most one another.
In this paper, we prove that each pseudo-outerplanar graph admits edge
decompositions into a linear forest and an outerplanar graph, or a star forest
and an outerplanar graph, or two forests and a matching, or
$\max\{\Delta(G),4\}$ matchings, or $\max\{\lceil\Delta(G)/2\rceil,3\}$ linear
forests. These results generalize some ones on outerplanar graphs and
$K_{2,3}$-minor-free graphs, since the class of pseudo-outerplanar graphs is a
larger class than the one of $K_{2,3}$-minor-free graphs.
