For real-time systems, multiprocessor support is indispensable to handle the large number of requests. Existing real-time on-line scheduling algorithms such as Earliest Deadline First Algorithm (EDF) and Least Laxity Algorithm (LLA) may not be suitable for scheduling real-time tasks in multiprocessor systems. Although EDF has low context switching overhead, it suffers from "multiple processor anomalies." LLA has been shown as suboptimal, but has the potential for higher context switching overhead. Earliest Deadline Zero Laxity (EDZL) solved somewhat the problems of those algorithms, however is suboptimal for only two processors. Another algorithm EDA2 shows very good performance in overload phase, however, is not suboptimal for muitiprocessors. We propose two on-line scheduling algorithms, Earliest Deadline/Least Laxity (ED/LL) and ED2/LL. ED/LL is suboptimal for multiprocessors, and has low context switching overhead and low deadline miss rate in normal load phase. However, ED/LL is ineffective when the system is overloaded. To solve this problem, ED2/LL uses ED/LL or EDZL in normal load phase and uses EDA2 in overload phase. Experimental results show that ED2/LL achieves good performance in overload phase as wet] as in normal load phase.oad phase.