I have a 1993 bmw 740il. It's in very good condition and works very well. But I have noticed that at highway speed its shakes. It usually starts gradually at a steady speed of 40 -45 and increases at 50-60. I don't usually drive faster than that so I don't know beyond that speed what it would do. Can you tell me what causes this an how it can be fixed?

This could be a tire issue. Tires can become out of balance or a belt can slip inside the tire. I would have the tires looked at by a professsional before doing anything else.

Sometime a wheel alignment will cure this. When was the last time you had a complete tune up ?

I will agree with all the above, from air pressure, bad tire, excessive wear on a tire or one section of a tire. And for sure an allignment.

Having your tires checked by a tire professional is where you start

Could be a broken motor or transmission mount or a driveshaft issue in addition to the tires as mentioned.

Well, I thought it could be the wheel but I had changed all the tires and rims on the vehicle and removed the factory wheels but it still gave the same problem. I also recently took it on a trip upstate and really ran the engine to clear it up and work so I got to 80 -90 and it didn't vibrate after I pass 60 going to 70 and beyond. I had also changed the control arms and thinking maybe to change the front struts