Rev Limiter/ Shift Problem

I recently purchased a 87' 560 SEC. Under hard acceleration or kick down the engine revs up to 5200 rpm then starts to stutter and stays at 5200, it will not upshift to 2nd. The fuel pump relay says 6000/min, is that the upper limit of the rev limiter? The tach shows a 6000 redline. The car has new plugs, idles smooth, good vacuum, excellent power right up to 5200 rpm then falls off the wall. I don't know if this is an engine/fuel problem or does the trans require a shift point adjustment. I have a 77"450 SL that pulls all the way to 6000 before shifting, but I don't think that it has a rev limiter.
thx, bob

my 500sec used to do the samething, before i sold it, wish i could solve the problem.