In this paper, we present a joint scheduling of hard deadline periodic and soft deadline aperiodic tasks in dynamic-priority systems. The proposed algorithm has extended the fixed-Critical Task Indicating (CTI) algorithm developed by the authors [3]. The dynamic-CTI algorithm is operated in such a way that dynamic-priority assignment strategy for a given periodic task set and the information on a deadlinewise preassignment table, called dynamic-CTI table, are mixed dynamically according to the aperiodic tasks' arrivals at runtime. The algorithm has a predictability and a less computational complexity in calculating the slacks since it uses the dynamic-CTI table. Our simulation study shows that the dynamic-CTI scheduling has better performance than the fixed-CTI algorithm which is even better than the slack stealing algorithms, especially under a heavy transient overload.