Method for operating a computer system

A method for operating a computer system including identical first and second processors operated in parallel and having at least two processor cores each, includes operating one processor core of each processor securely based on a secure operating system achieving or exceeding a specified security level, each executing at least one application program securely by achieving the specified security level. The processor cores securely execute the same application program or programs. Remaining processor cores of the first processor are switched off or operated securely, based on the secure operating system or one or more other secure operating systems under the secure execution of the same and/or other application programs. At least one processor core in the second processor is operated nonsecurely based on a nonsecure operating system not achieving the specified security level and executes at least one application program nonsecurely, falling short of the specified security level.