  In this article we study minimal flat Lorentzian surfaces in Lorentzian
complex space forms. First we prove that, for minimal flat Lorentzian surfaces
in a Lorentzian complex form, the equation of Ricci is a consequence of the
equations of Gauss and Codazzi. Then we classify minimal flat Lorentzian
surfaces in the Lorentzian complex plane ${\bf C}^2_1$. Finally, we classify
minimal flat slant surfaces in Lorentzian complex projective plane $CP^2_1$ and
in Lorentzian complex hyperbolic plane $CH^2_1$.
