Rokhlin's complex orientations of a real algebraic curve dividing its complexification
are generalized to real algebraic surfaces. First, the notion of type of a real
allegoric curve is generalized. In place of two type (curves dividing and non-dividing
their complexifications) we consider three types: I absolute, I relative and II.
A surface belongs to type I absolute, if its real part is zero-homologous modulo 2
in the complexification. A surface is of type I relative, if its real part is homologous
modulo 2 to the class of hyperplane section. In other cases it is of type II. For a
surface of type I absolute a pair of opposite to each other orientations of the set
of real points is defined. For a surface of type I relative, the set of real points
is oriented in the complement of a hyperplane section. At the end of the paper similar
Spin- and Pin- structures are defined for surfaces of type I absolute and I relative,
respectively.