  In this paper, we study degenerate almost complex surfaces in the
semi-Riemannian nearly K\"ahler $\mathrm{SL}_2\mathbb{R}\times
\mathrm{SL}_2\mathbb{R}$. The geometry of these surfaces depends on the almost
product structure of the ambient space and one can distinguish two distinct
cases. The geometry of these surfaces is influenced by the almost product
structure of the ambient space, leading to two distinct cases. The first case
arises when the tangent bundle of the surface is preserved under the almost
product structure, while the second case occurs when the tangent bundle of the
surface is not invariant under this structure. In both cases, we obtain a
complete and explicit classification.
