Recently, researchers have shown increasing interest in combining more than one programming model into systems running on high performance computing systems (HPCs) to achieve exascale by applying parallelism at multiple levels. Combining different programming paradigms, such as Message Passing Interface (MPI), Open Multiple Processing (OpenMP), and Open Accelerators (OpenACC), can increase computation speed and improve performance. During the integration of multiple models, the probability of runtime errors increases, making their detection difficult, especially in the absence of testing techniques that can detect these errors. Numerous studies have been conducted to identify these errors, but no technique exists for detecting errors in three-level programming models. Despite the increasing research that integrates the three programming models, MPI, OpenMP, and OpenACC, a testing technology to detect runtime errors, such as deadlocks and race conditions, which can arise from this integration has not been developed. Therefore, this paper begins with a definition and explanation of runtime errors that result fromintegrating the three programming models that compilers cannot detect. For the first time, this paper presents a classification of operational errors that can result from the integration of the three models. This paper also proposes a parallel hybrid testing technique for detecting runtime errors in systems built in the C++ programming language that uses the triple programming models MPI, OpenMP, and OpenACC. This hybrid technology combines static technology and dynamic technology, given that some errors can be detected using static techniques, whereas others can be detected using dynamic technology. The hybrid technique can detect more errors because it combines two distinct technologies. The proposed static technology detects a wide range of error types in less time, whereas a portion of the potential errors that may or may not occur depending on the operating environment are left to the dynamic technology, which completes the validation.