The integration of both real-rime systems and fault-tolerant systems h
as been emerged as one of the greatest challenges of this decade. It i
s called a responsive system, which has the objective to optimize both
timeliness and reliability. The performance measure in responsive sys
tems is responsiveness that tells how probable a system executes corre
ctly on time with faults occurred. While there have been some achievem
ents in communication protocols and specification, we believe that sch
eduling problems in responsive systems are not understood deeply and s
ufficiently, yet. In this paper, we discuss the scheduling problem in
responsive systems. At first, we investigate the issues in the schedul
ing and propose the precise definition of the responsiveness. We also
suggest a scheduling algorithm called Responsive Earliest Deadline Fir
st (REDF) for preemptive-aperiodic tasks in a uniprocessor system. We
show that REDF is optimal to obtain the maximum responsiveness, and th
e time complexity is analyzed to be O (N x 2(N)). By illustrating a co
ntradictory example, it is shown that REDF can be enhanced if a constr
aint on tasks is released.