My grill also smokes - so badly I can't even use it?

I am now on my second combined built in oven/grill and they have both smoked so badly after using the grill only a few times that I can't use it. The acrid smoke that comes out is horrible and you can't breathe. The first cooker was with the house when we moved in so we bought a new one but this is just as bad! You can't remove the heated element at the top to clean it so I can't try and solve this. The first model was a Creda and the second is a Bosch. Could it be that there is no ventilation behind? Help!