  We consider Lorentz surfaces in $\mathbb R^3_1$ satisfying the condition
$H^2-K\neq 0$, where $K$ and $H$ are the Gauss curvature and the mean
curvature, respectively, and call them Lorentz surfaces of general type. For
this class of surfaces we introduce special isotropic coordinates, which we
call canonical, and show that the coefficient $F$ of the first fundamental form
and the mean curvature $H$, expressed in terms of the canonical coordinates,
satisfy a special integro-differential equation which we call a natural
equation of the Lorentz surfaces of general type. Using this natural equation
we prove a fundamental theorem of Bonnet type for Lorentz surfaces of general
type. We consider the special cases of Lorentz surfaces of constant non-zero
mean curvature and minimal Lorentz surfaces. Finally, we give examples of
Lorentz surfaces illustrating the developed theory.
