Civic headlight problem

When I turn on the headlights in my 98 Civic CX, there is a delay before the lights come on. Originally they worked fine, then the delay started. Initially it was approx 5 seconds but is getting much longer. All the other lights on the car work fine, including the daytime running lights. Even the high beams work ok when I flick the indicator while waiting for the headlights to come on. I fear one of these days the lights will not come on at all. Any advice on what is causing this problem?