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High availability is a key requirement in the design and development of heterogeneous systems where processors operate at different speeds and are not continuously available for computation. Most existing scheduling algorithms designed for heterogeneous systems do not factor in availability requirements imposed by multiclass applications. To remedy this shortcoming, we investigate in this paper the scheduling problem for multiclass applications running in heterogeneous systems with availability constraints. In an effort to explore this issue, we model each node in a heterogeneous system using the node's computing capability and availability. Multiple classes of tasks are characterized by their execution times and availability requirements. To incorporate availability and heterogeneity into scheduling, we define new metrics to quantify system availability and heterogeneity for multiclass tasks. We then propose a scheduling algorithm to improve the availability of heterogeneous systems while maintaining good performance in the response time of tasks. Experimental results show that our algorithm achieves a good trade-off between availability and responsiveness.