Oil pressure guage pegs out when I accelerate--WHY

Remove the oil pressure switch. It is typically located near the oil filter. Install the appropriate fitting from the oil pressure gauge kit. Install the gauge. Start the vehicle.

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Whats the make and model? Depending on what you are driving it sounds like either your oil filter is plugged up and you need an iol change, you have oil that is too thick in there, too much oil, or possably a clog in the oil pump or paths running to and from that area

The guage may rise a little when you accelerate the vehicle...but if it is pegged high, and does not fluctuate, when you turn your ignition key on an off...Your oil pressure switch maybe going bad...Goodluck

it could be the sensor you should look at the oil pressure relief valve

You may have a Faulty Oil Pressure Sender.
Here are some reason why your guage is bouncing:

• Corrosion or faulty electrical connections
• If the oil pressure gauge is pegged low after the engine is running, or is pegged high after the engine is running, or if there is intermittent illumination of an oil pressure indicator light, the sender could be faulty

You can find the oil sensor on the left hand side near the Oil Filter, as long as you don't hear your lifters ticking and making lots of noise. it's not your oil pump failing. 
Good luck and hope this helps

Try replacing the oil pressure sending unit

sounds to me like you have a bad oil pressure sinding unit

The sending unit would be the first thing to change, at least it would eliminate that.

OIL SENDING UNIT. JEEPS ARE NOTOROIUS WITH THIS PROBLEM

YES this is where I would start ALONG WITH A MANUAL PRESSURE TEST if Sending unit doesnt and Pressure test is GOOD ,Replace the Meter in Insrtament Cluster
I Have Pics but they will not show up in FixYa
The Oil Pressure sensor is on the Back of engine Looks like Left side 3 wire plug on 4.8L 5.3L 6.0L Can Email Pic with your Address