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There is an increase in deploying Deep Learning (DL)-based software systems in real-world applications. Usually DL models are developed and trained using DL frameworks that have their own internal mechanisms/formats to represent and train DL models, and usually those formats cannot be recognized by other frameworks. Moreover, trained models are usually deployed in environments different from where they were developed. To solve the interoperability issue and make DL models compatible with different frameworks/environments, some exchange formats are introduced for DL models, like ONNX and CoreML. However, ONNX and CoreML were never empirically evaluated by the community to reveal their prediction accuracy, performance, and robustness after conversion. Poor accuracy or non-robust behavior of converted models may lead to poor quality of deployed DL-based software systems. We conduct, in this paper, the first empirical study to assess ONNX and CoreML for converting trained DL models. In our systematic approach, two popular DL frameworks, Keras and PyTorch, are used to train five widely used DL models on three popular datasets. The trained models are then converted to ONNX and CoreML and transferred to two runtime environments designated for such formats, to be evaluated. We investigate the prediction accuracy before and after conversion. Our results unveil that the prediction accuracy of converted models are at the same level of originals. The performance (time cost and memory consumption) of converted models are studied as well. The size of models are reduced after conversion, which can result in optimized DL-based software deployment. Converted models are generally assessed as robust at the same level of originals. However, obtained results show that CoreML models are more vulnerable to adversarial attacks compared to ONNX.