Many computer systems, such as those for open system environments or multimedia services, need an efficient schedulability test for online admission control of new jobs. Although various polynomial time schedulability tests have been proposed, they often fail to decide the schedulability of the system precisely when the system is heavily loaded. On the other hand, most precise schedulability tests proposed to date have a high complexity and may not be suitable for online tests. We present new efficient online schedulability tests for both the periodic process model [C. L. Liu et al., (1973)] and the multiframe process model [A. K. Mok et al., (1997)] in uniprocessor environments. The schedulability tests are shown to be more precise and efficient than any existing polynomial-time schedulability tests. Moreover, the tests can be done incrementally as each new task arrives at the system. Our proposed tests can also be used for the multiframe model where a task may have different computation times in different periods. We show the performance of the proposed schedulability tests in several simulation experiments.