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The vehicular edge computing (VEC) can cache contents in different RSUs at the network edge to support the real-time vehicular applications. In VEC, owing to the high-mobility characteristics of vehicles, it is necessary to cache the user data in advance and learn the most popular and interesting contents for vehicular users. Since user data usually contains privacy information, users are reluctant to share their data with others. To solve this problem, traditional federated learning (FL) needs to update the global model synchronously through aggregating all users' local models to protect users' privacy. However, vehicles may frequently drive out of the coverage area of the VEC before they achieve their local model trainings and thus the local models cannot be uploaded as expected, which would reduce the accuracy of the global model. In addition, the caching capacity of the local RSU is limited and the popular contents are diverse, thus the size of the predicted popular contents usually exceeds the cache capacity of the local RSU. Hence, the VEC should cache the predicted popular contents in different RSUs while considering the content transmission delay. In this paper, we consider the mobility of vehicles and propose a cooperative Caching scheme in the VEC based on Asynchronous Federated and deep Reinforcement learning (CAFR). We first consider the mobility of vehicles and propose an asynchronous FL algorithm to obtain an accurate global model, and then propose an algorithm to predict the popular contents based on the global model. In addition, we consider the mobility of vehicles and propose a deep reinforcement learning algorithm to obtain the optimal cooperative caching location for the predicted popular contents in order to optimize the content transmission delay. Extensive experimental results have demonstrated that the CAFR scheme outperforms other baseline caching schemes.