Abstract: Unstable zeros limit the achievable control performance. When a continuous-time system is discretized using the zero-order hold, the stability of zeros cannot be reserved. This paper analyzes the asymptotic properties of the limiting zeros of discrete-time system corresponding to continuous-time MIMO plants with the degrees of infinite elementary divisors being two or three. The linear approximate expressions with respect to the asymptotic behavior of the limiting zeros are given. The conditions that ensure the stability of the limiting zeros of discrete-time systems for sufficiently small sampling periods are derived and proved in detail. It is a further extension of Ishitobi's result.