No, it is not legal for the corporation to continue doing business in California without having an agent for service of process. In California, as in most all states, all foreign corporations -- which, less exotically, means all corporations formed in another state -- must have agents for service of process if they conduct any business in the state. An out-of-state corporation has to designate an agent before it begins doing business in California, file a statement every year identifying its agent, and file an amended designation if the name or address of the agent changes.

You don't have to serve the agent, however: You can also serve any officer of the corporation or its general manager. And if you cannot find the agent, an officer, or the general manager, you may serve the corporation by delivering the papers to California's Secretary of State -- all corporations must register with the Secretary of State before doing any business in California. To take this last route, though, you must first get a court order allowing it; you will be required to show that you tried without success to locate the agent for service of process.