  We classify different theories of self-intersecting random surfaces assigning
special weights to intersections. When self-intersection coupling constant
$\kappa$ tends to zero, then the surface can freely inetrsect and it is
completely self-avoiding when $\kappa$ tends to infinity. Equivalent spin
systems for this general case were constructed. In two-dimension the system
with $\kappa = 0$ is in complete disorder as it is in the case of 2D gauge
Ising system.
