  The properties of gravitational kinks are studied within some simple models
of two dimensional gravity. In spacetimes of cylindrical topology we prove the
existence of kinks of constant curvature with arbitrary kink numbers. In
$R^1\times R^1$ spacetimes $m=1$ kink solutions of the equation $R=0$ are
found, whereas $|m|>1$ flat kinks are proved not to exist. We give a detailed
analysis of the behaviour of gravitational kinks under coordinate
transformations. Viewed as nonsingular black holes $|m|>1$ kink solutions are
found within a simple dilaton gravity theory. The general form of the potential
function is determined from the demand that the theory possesses an arbitrary
number of inequivalent kink configurations.
