Hesitation for first 100-200' of driving, then fine?

Hey, everyone. Having some weird issues as of late and I'm looking for some other view on them if you're up for it.

#1
Each time I start the Jeep it idles fine, no issues there. I can open the throttle and it will respond just fine while stationary. However, once I start moving down the road it will hesitate and gradually lose power, make a faint popping noise, then accelerate. It repeats this about 5x or for the 1st 100-200', then suddenly accelerates and acts normal.

#2
At cruising highway speeds, my RPMs will fluctuate by about 200-300 sporadically. I can put it in cruise @ 60mph turning 2500RPM and it will randomly open up to 2750-2850 for a few seconds then settle back. It'll do this every few minutes at random.

What I've replaced:
Fuel pump - last week
Fuel filter - last week
Distributor cap - last week
Rotor button - last week
Spark plugs & wires - about 8-9 months ago
CPS - about a year ago, tested it last week and it's fine
Air filter is also fine

Thoughts?

What year/engine?

Throttle position sensor is a possibility. It is directly involved with fuel delivery. They can be tested and depending on the year, yours may need adjustment (87-90)

Test the Throttle Position Sensor.

Whoops, can't believe I forgot the basics: 96 4.0 with AW4

Update: replaced TPS, same thing still happens and now my CE light is showing voltage for the TPS is too high/too low. I'm going to exchange it for another unit. Any ideas in the meantime?

I'd be interested to see what you come up with as a solution. My GF's 97 TJ does the same exact thing. I have heard people say that they tried parts stores sensors will no luck then decided to buy one from the dealer and it fixed it. Just an idea.

I had the same thing happen a lot a while ago. I tried replacing the TPS, didn't help, tried a brand new one, didn't help. Hasn't happened in like a year and a half, I'm pretty sure disconnecting and reconnecting all the electrical stuff during my drivetrain swap a while ago (pulled whole drivetrain, put new tranny in the middle, reinstalled) cleaned up a random dirty connection somewhere.

The RPM spiking issue is your torque converter lockup turning off and then back on. Probably related to the same thing as the hesitation, i.e. the TPS. Clean all your connections and see what happens. It could also be a brake light switch issue though, if the TCU sees its contact in the brake pedal switch change it will unlock the torque converter.

Just a quick update:
Hesitation after start up has almost completely gone away. Sensor stopped giving CEL after a day or so and has seemingly been working fine. I found two small hoses that look like they could be providing a bit of a vacuum leak at the intake manifold, will replace and see if the converter unlocking stops. I'll post back when I get a chance.

Another update: hesitation came back. Was reading more about those symptoms and saw an article pointing to the upstream O2 sensor. Replaced it and sure enough, that was it.

Mine was doing the very exact same thing when the upstream sensor went out last week. Surprised you didn't have a CEL. Glad you got it fixed.. I'm sure your gas mileage went up.