This chapter is concerned with asymptotic stability analysis of neutral type time-delay positive systems (TDPSs). We focus on a neutral type TDPS represented by a feedback system constructed from a finite-dimensional LTI positive system and the pure delay, and give a necessary and sufficient condition for the stability. In the case where we deal with a retarded type TDPS, i.e., if the direct-feedthrough term of the finite-dimensional LTI positive system is zero, it is well known that the retarded type TDPS is stable if and only if its delay-free finite-dimensional counterpart is stable. In the case of neutral type TDPS, i.e., if the direct-feedthrough term is nonzero, however, we clarify that the neutral type TDPS is stable if and only if its delay-free finite-dimensional counterpart is stable and the direct-feedthrough term is Schur stable. Namely, we need additional condition on the direct-feedthrough term.