1990 740GL stalling and hesitation issues

[marinwood]

I recently got this nice car. Golden brown; all leather; sedan.
All runs good on it except when going over 55mph on highways when there are some hills or slowing down from high speed;
the engine coughs and hesitates and eventually cuts all power and stalls with all lights coming on.
Then after a minute or so the engine can come back on with no problem to start.
Even while on level road on highway speeds the engine is hesitating after 55mph or higher speeds but usually keeps going.
Any idea what the cause may be? I have full gas tank and on low speeds the car has reasonable power and no hesitation.
Hopefully not transmission related as it seems to come on while in the highest gear (overdrive on).
Any help would be welcome. I really would like to keep the car without putting in some major work at the beginning already.
It needed a starter only so far that cost way less than my 850 Turbo`s starter.

[billofdurham]

Have any fault codes been set?

Is the in-tank fuel pump working? The main pump can usually cope on its own with a full fuel tank but it does struggle when accelerating when more power is called for.

Bill.