I'd try the starter if there are no black bands at either end. Otherwise it is the ballast that needs to be replaced.

Quote:
When fluorescent lights begin flickering, it is a warning sign that something is amiss. It might be one of three things; worn-out tubes, a failing ballast, or a failing starter. When fluorescent bulbs get old, their ends darken and they begin flickering. Once this occurs, the bulbs should be replaced. If the fixture has multiple tubes or is installed in a hard-to-reach location, it's best to replace all the tubes at the same time.

Worn starters can also cause flickering. They are seldom found on newer fluorescent lights but are quite common on older models. They are a short metal cylinder with two contacts on one end. They are plugged into the fixture and supply the initial jolt of electricity that lights the tubes. They are easy to locate and replace. If you suspect your starter is failing, take it along when you buy the replacement. There are several models, and while they are the same size and shape, the wattage of the tubes in your fixture determines which one you will need.

The third cause of flickering is a failing ballast. Ballasts perform the same function as starters and are frequently found in multi-tube fluorescent fixtures. They are also easy to replace, but can be very expensive. Prices range from $14 to $75. For the price of a new ballast, you might be able to buy a new fixture and tubes.


Read more: DIY Fluorescent Lighting Repairs | eHow.com http://www.ehow.com/way_5618429_diy-fluorescent-lighting-repairs.html#ixzz15BVTqSl6

And here is some info about replacing the ballast.
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