1. A data processing system which performs a plurality of processes sequentially, said data processing system comprising: program memory means for storing therein a plurality of task programs which correspond to respective tasks; execution means for executing one of the tasks based on a corresponding one of the plurality of task programs stored in said program memory means, wherein each of the plurality of processes is performed by executing several of the tasks and some of the tasks are executed commonly in different processes; flag storage means for storing first flags each corresponding to respective malfunctions of said data processing system and respective user's operations, second flags each corresponding to respective statuses of performance of the plurality of processes and groups of third flags each of the groups corresponding to respective processes and each of a third flag corresponding to respective statuses of execution of tasks in the plurality of processes; flag management means for setting flags in response to an occurrence of respective malfunctions and respective user's operations and at a start of respective tasks, and resetting each of the flags in response to an end of execution of respective tasks; first check means for checking the first flags and the second flags in a predetermined order until a set flag is located in response to an end of execution of each task; first scheduling means for selecting one of the plurality of processes to be performed next in accordance with a set first flag if one of the first flags is found to be set by said first check means or in accordance with a set second flag if one of the second flags is found to be set by said first check means; second check means for checking the third flags of a group corresponding to a process selected by said first scheduling means in a predetermined order until a set flag is located in response to the end of the execution of each task; second scheduling means for selecting a task to be executed next among tasks corresponding to the process selected by said first scheduling means in accordance with a third flag found to be set by said second check means; and control means for controlling said execution means to execute a task selected by said second scheduling means.