What causes my vehicle to pull to one direction only when I throttle at high speed?

I have a 1988 Pathfinder. The vehicle coasts straight and true, and there are no signs of tire wear (10K+ miles on tires). The vehicle pulls to one side only when I throttle. I don't notice this when I am constantly on the throttle, but only when I alternate between coasting and accelerating. I have to compensate the steering wheel, and when going fast, this can really cause me to be swervy. I don't want to be pulled off the road for looking like I am driving drunk, or worse yet, skid off the road in snowy conditions. Is this an alignment problem?