By an oval in $${\mathbb {Z}}^2_{2p},$$
Z
2
p
2
,
p odd prime, we mean a set of $$2p+2$$
2
p
+
2
points, such that no three of them are on a line. It is shown that ovals in $${\mathbb {Z}}^2_{2p}$$
Z
2
p
2
only exist for $$p=3,5$$
p
=
3
,
5
and they are unique up to an isomorphism.