Celica steering wheel vibration - what's the cause?

I own a 2004 Toyota Celica and I'm having endless problems with vibration coming through the steering wheel at around 70mph. The front and rear wheels have been balanced (the fronts by two different garages) but it hasn't cured the problem.

It has done 88,000 miles and the suspension seems in good order, with no knocks or rattles or uneven tyre wear. The front wheels are new and also the tyres so I'm confident they are not buckled. Do you have any idea what might be wrong?

Asked on 17 December 2013 by Sam

Answered by Honest John
Well, it could be driveshafts. But first, assuming the front and rear tyres are the same size, try swapping front to back. There's just a chance it may work.
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