Nissan power cuts out when I step on gas

Exhaust blockage will cause that to happen.

too serious a problem to let go un-diagnosed
pop into the service center for assessment

is the engine light on
that model has an electronic gas pedal sensor
I would start there

then if motor revs a lot and not go forward as it should
a transmission fault

Could be anything from air leak(s) to fuel pressure or injector spray patterns or even the onset of valve problems.

I suggest starting with a tuneup and hope the result is good. If not the tuneup should provide clues where to look for the actual fault(s).

I did say faults because when a car has had 20 years of service and it has a problem, the problem is often a combination of more than one "nearly" fault and perhaps several that adds up to a Problem.

If this is a deisel then it's probably some sensor malfunction. It could be one of the sensors in the exhaust system or a simple electrical fault - I have been told it can happen if even just one brake-light bulb is broken

they are correct change the fuel filters

sending unit is bad or thermostat is stuck open

it needs a complete fuel cleanning anad a tune up

i would start by checking the mass air flow sensor or put a scan tool and checking live data.long trim and short trim fuel. may need a dealerfor that.

could be your (air flow meter,,)they give alot of trouble on nissans...unplug it and if it runs a bit better then thats it,,,

Fuel problem or the ECM and or chip has a 80mph limiter. Or your really winding out the engine, in which case, by the time you read this it will be too late.