Systems such as coordinating robot systems, automobiles, aircrafts, and chemical process control systems can be modeled as interacting hybrid systems, where hybrid systems are finite state machines with continuous dynamics. The language CHARON and its simulator have been developed to model and analyze interacting hybrid systems as communicating agents. Simulations are widely used for the analyses of hybrid systems. The simulation of a complex system is, however, usually very slow. This paper proposes four algorithms for distributed simulations of hybrid systems. The idea behind distributed simulations is to achieve a speedup by utilizing multiple computing resources. The agents of a modeled system are distributed over multiple processors to simulate the agents more efficiently. Since the state of the agent is affected by the input from other agents, they synchronize to update their local states. The challenge here is how to reduce the agent synchronization overhead. We present two approaches for resolving the problem: conservative and optimistic approaches. For the optimistic approach, we present three different algorithms for distributed simulations of hybrid systems, and compare them.