I bought a used car and now the vehicle is spontaneously accelerating but there is no recall, what can I do?

First, you need to address the safety issue. Since your state's lemon law only covers new vehicles, it does not cover you; that means that you ability to force the manufacturer or dealer to make repairs is limited (though you may be able to get reimbursement or compensation; see below). Therefore, you should see first about having the repair or fix made, so you don't endanger you life or others' lives; then see about seeking payment.

Second, as to a possible legal action: if the problem is that the car was designed or manufactured improperly, you may have a cause of action against the manufacturer for a defective product. If the car was not designed or manufactured improperly though, but rather developed a problem later, the manufacturer would likely not be liable.

If the dealership or other person from whom you bought the car was aware of the acceleration problem (regardless of cause), you may be able to sue that person in fraud--for either misrepresenting (lying) about critical information, or for improperly omitting to provide critical information which any buyer would want and any seller should disclose. However, if the person did not know about the problem (e.g. didn't happen to him; developed later; etc.), he would not be liable.

Therefore, you *may* have one or two grounds to seek compensation, but it depends on the facts. Again, though, his is likely a case where you need to address safety issues first; if you don't, besides the risk to life  and limb, if you are in an accident, you would almost certainly be liable, for continiuing to drive a car with a known safety issue.