The neutral delay model has many applications in biology, ecology, man-made neural networks, mechanics and engineering. The main purpose of this paper is to establish new oscillation criteria for the two-dimensional neutral delay dynamical system [Formula: see text] on a time scale [Formula: see text], where [Formula: see text] and [Formula: see text] are positive rd-continuous functions, [Formula: see text], are in accordance with the definition given by S. H. Saker, Oscillation of nonlinear dynamic equations on time scales, Appl. Math. Comput. 148 (2004) 81–91.