In response to the last two posts:

My mechanic says that he has seen many 740's with antifreeze in the trans and so is familiar with the problem. As he has taken the trans apart three times now and checked the fluid, he says there was definitely no antifreeze in it.

Regarding codes, no codes for the engine or trans have ever appeared. However, he still is interested in checking the engine, e.g., injectors, throttle body, and anything else that might cause a hesitation.

Regarding 2nd gear acceleration, my original post meant to say the the car had gone from 1st to 2nd when the hesitation occurred, rather than starting from a stop in 2nd.

There has been an improvement in driving the last few days. No problems at all. This is very confusing. I think the next step will be to have a thorough engine check. BTW a year ago we had an intermittently-stuck butterfly valve with no code that caused stalling and a major headache.

Thanx for you help. Any other ideas are definitely welcome.