Just kidding; it's not that simple; technically a 1983 claim doesn't have a statute of limitations per se, but 42 USC 1988(a) requires federal courts to borrow a state's limitation period. So every state is different. When the cause of action accrues (basically begins to run) is a question of federal law. Oversimplifying a cause of action accrues when the plaintiff knows or has reason to know of the injury that is the basis of his or her claim. So in a wrongful termination case, the cause of action accrues when the plaintiff is notified that he is being canned; not the effective date of the termination. I don't know what you're legal background is, if any, but many attorneys get themselves in trouble be delving into this arena--be careful and good luck.
Absolutely there are statute of limitations on civil rights claims. There is also a requirement that makes you file a claim with the State (sometimes w/i 6 months time period. The Federal 1983 statutes of limitation depend upon the state statute of limitation. So, if Juan wants to sue the police department for a 1983 action in court, Juan has 2 years from the date of the incident to file that federal claim (the 2 years came from California's 2 yr SOL for personal injuries. If you have a case, I would talk to an attorney in your area asap. The Govt Tort Act is tricky in California. If you're in Cal, you can email me and I might be able to get you started.