'01 540i RPMS slowly drop while driving

[rdl]

Well, I said I'd come back when I tracked the problem down. I'm glad to say that I resolved this by changing the transmission fluid and filter. I didn't think that was the issue since this had been done about 40,000 miles ago
...

Thanks for the follow-up. So many don't bother.

I think it would be useful to all of us to know which brands of filter & ATF you used "before" and "after." And also which brand & model transmission?

[BlKdOuT]

I changed the trans fluid and filter.
Still have same issue.

[bimmer7410]

I changed the trans fluid and filter.
Still have same issue.

So you get the periodic dips in RPM while at highway speed. Do you hear any sounds that accompany this?

[edjack]

Did you replace all the fluid, or just what was in the pan?

[BlKdOuT]

Yes while at highway speed under slight acceleration.
No noises at all.
I changed the fluid just once so far so just what was in the pan.

Will be changing it again soon. I have read it takes about 3 changes to get all old fluid out.

I am using the pentosin fluid and OEM filter so not the cheapest to do.