The lightlike geometry of codimension two spacelike submanifolds in Lorentz–Minkowski space has been developed by Izumiya and Romero Fuster (Selecta Math (N.S.) 13:23–55, 2007) which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we investigate a special class of surfaces (i.e., marginally trapped surfaces) in Minkowski space-time from the view point of the lightlike geometry.