In reply to stella1: I worked as a Peugeot car salesman in a dealership for a year.
Finance approval for someone with a fairly clean credit rating is instant or within a couple of hours.
The dealership are desperate for the sale, so if someone is not getting approved, it gets special attention and will be looked at by the finance company and they will try everything possible to get a deal together.
Even with difficult cases, it shouldn't take more than a couple of days. If it's been two days, definitely give them a call.