Among 60 to 80 km/h the front of the car vibrates sidelong, but to stop the acceleration the vibration it disappears and to accelerate the vibration again returns.

 

I had a similar problem with my 94 Caravan, Turns out that my front tire was "Out of round" and more shapped like an Egg. Try jacking up the side that is giving you the problem, and spinning the wheel around make sure it is indeed round

 

Check the spark plugs and wires.They do wear out.