— The generalized multiframe (GMF) task has been proposed to model a task whose execution times, deadlines and minimum separation times are changed according to a specified pattern. In this paper we relax the assumption of having a specified activation pattern, this yields to non-cyclic GMF task. In this context, current schedulability analysis techniques for GMF task sets under dynamic priority assignment cannot be used. This paper presents response time analysis of non-cyclic GMF tasks executing on a uniprocessor according to earliest deadline first (EDF) scheduling policy. Also, a density-based sufficient schedulability test for noncyclic GMF task sets is given. Finally an efficient approach is presented, for exact feasibility determination using computer simulation. Keywords-component: schedulability analysis, non-cyclic GMF task, EDF.