There is a growing demand for accurate dynamic models, driven by the Industry 4.0 paradigm that introduces, among others, the concept of the digital twin in which dynamic models play an important role. Ideally, a dynamic model presents a compromise between complexity and accuracy, while providing physical insight into the system. To improve a model accuracy while keeping interpretability, the usual approach is to mathematically model all the nonlinearities, which ultimately leads to an overcomplex model. Another approach involves a black-box identification, a data-driven approach where a mathematical model is adjusted to describe the system s input-output relation, which may provide an accurate model, but it does not provide interpretability. The developments in computational processing capacity have allowed the flourishing of the field of machine learning, which has shown interesting results in different fields of knowledge. One of these applications is black-box identification, where machine learning has successfully been employed in the modeling of nonlinear systems, which has inspired research on the topic. Even though the machine-learning-based models present enhanced accuracy, which for several applications is sufficient, they do not provide interpretability. Aiming at providing both accuracy and interpretability while keeping a compromise with model complexity, this work proposes a hybrid identification methodology that combines a gray-box phenomenological model with a black-box model based on artificial neural networks. The proposed methodology is applied in three case studies of nonlinear systems with experimental data, namely, the vertical dynamics of a vehicle, an elastomer-based series elastic actuator, and an electromechanical positioning system. The results show that the proposed hybrid model is up to 60 percent more accurate while providing the physical interpretability of the system, without significantly increasing the complexity of the model.