In this paper, we establish some new oscillation theorems for neutral higher order functional differential equations of the form (E)\(\frac{{d^n }}{{dt^n }}(x(t) + cx(t - h) + Cx(t + H)) + qx(t - g) + Qx(t + G) = 0,\) wherec, C, g, G, h andH are real constants, andq andQ are nonnegative real constants. The results of this paper improve noticeably the known oscillation theorems. By a new analysis technique we give weaker sufficient conditions for all solutions of equation (E) to be oscillatory.