The problem was that during uphill and on the top level, instead of gaining speed this was not possible for auto was unresponsive to shift to higher gear ( giving higher RPM). This has brought me to a

That is normal for that year models, I think. Earlier cruise control just maintains the engine RPM in relation to speed. It does not use auto braking to reduce downhill speeds. Best way is to get it scanned with diagnostic scanner that can reset or check error codes for cruise control.

This vehicle had option of three different transfer case ! Which one of these is the one in your vehicle ?
Transfer Case - NVG 120-NR9 Transfer Case - NVG 126-NP4 Transfer Case - NVG 226-NP8
The New Venture Gear model NVG 226 RPO NP8 transfer case is a two speed automatic, active, transfer case. The NVG 226 provides five modes, Auto 4WD, 4 HI, 4 LO, 2 HI and Neutral. The Auto 4WD position allows the capability of an active transfer case, which provides the benefits of on-demand torque biasing wet clutch and easy vehicle tuning through software calibrations. The software calibrations allow more features such as flexible adapt ready position and clutch preload torque levels. The technology allows for vehicle speed dependent clutch torque levels to enhance the performance of the system. For example, the system is calibrated to provide 0-5 lb ft of clutch torque during low speed, low engine torque operation, and predetermined higher torque for 32 km/h (20 mph) and greater. This prevents crow-hop and binding at low speeds and provides higher torque biases at higher vehicle speeds, to enhance stability.
The New Venture Gear model NVG 126 RPO NP4 transfer case is a one speed automatic, active, transfer case. The NVG 126 provides only one mode, Auto 4WD, and is transparent to the operator. The active transfer case provides the benefits of on-demand torque biasing, wet clutch and easy vehicle tuning through software calibrations. The software calibrations allow more features, such as flexible adapt ready position and clutch pre-load torque levels. The technology allows for vehicle speed dependent clutch torque levels to enhance the performance of the system. For example, the system is calibrated to provide 0-7 N?·m (0-62 lb in) of clutch torque during low speed, low engine torque operation, and predetermined higher torque for 32 km/h (20 mph) and greater. This prevents crow-hop and binding at low speeds, and provides higher torque biases at higher vehicle speeds, to enhance stability
The New Venture Gear (NVG) model NV120, RPO NR9 transfer case is a single speed, full-time, all wheel drive (AWD), transfer case that incorporates a front/rear drive differential carrier assembly.

The NVG 263 transfer case features a three button shift control switch located on the instrument panel. When the ignition is in the RUN position, the transfer case shift control module (TCCM) starts monitoring the transfer case shift control switch to determine if the driver desires a new mode/gear position. At a single press of the transfer case shift control switch, the lamp of the new desired position begins flashing to inform the driver that the TCCM has received the request for a new mode/gear position. The lamp continues to flash until all shifting criteria has been met and the new mode/gear position has been engaged. Once the new mode/gear position is fully active, the switch indicator for the new position remains ON constantly. In the event that the TCCM can not or will not complete the shift, the indicator returns to the previously selected position; this is a Transfer Case Shift Control Switch Indicator Flashes, then Returns to Previous Mode condition.
The New Venture Gear model NVG 246 RPO NP8 transfer case is a two speed automatic, active, transfer case. The NVG 246 EAU provides 5 modes, Auto 4WD, 4HI, 4LO, 2HI and Neutral. The Auto 4WD position allows the capability of an active transfer case, which provides the benefits of on-demand torque biasing wet clutch and easy vehicle tuning through software calibrations. The software calibrations allow more features such as flexible adapt ready position and clutch preload torque levels. The technology allows for vehicle speed dependent clutch torque levels to enhance the performance of the system. For example, the system is calibrated to provide 0-5 ft lb of clutch torque during low speed, low engine torque operation, and predetermined higher torque for 40 km/h (25 mph) and greater. This prevents crow-hop and binding at low speeds and provides higher torque biases at higher vehicle speeds, in order to enhance stability.

When a car is going uphill, it has to use more power to get up the hill. Most automatic transmission cars will automatically detect this, and shift into a lower gear to get the car up the hill easier. As you get to the top or let off the gas, the car should than shift into a higher gear to maximize fuel efficiency. What does your transmission seem to do? Not want to go into a lower gear, are the RPMs jumping up and down before it shifts?

catalytic converter. get it tested. Might be the fuel filter clogging up.

Mitsubishi automatic transmissions can be finicky when it comes to there fluid. If it has not been changed for a while get some Diamond SP III ATF or a synthetic equivalent and change the automatic transmission fluid. It may clear up minor shifting issues that are caused by old tired fluid.

It could be the fuel pressure regulator valve is at fault. Maybe its time to have a fuel pressure diagnostic run along with having the injectors flushed. How is the transmission fluid level looking, check it on the transmission dipstick whilst the engine is running (have someone engage 'drive' while both the parking and foot brakes are engaged). If it is brown and low replace the transmission filter and top up with fresh fluid

Hi, two possible issues here. the first could be a malfunctioning shift solenoid. this can affect the shifting operation. the next issue could be the transmission control model(TCM). if this fails, you will experience abnormal shifting during up and downshifting. I would check these areas as well as the fluid level as well. Some transmissions are sealed and you cant check the fluid level. if you have a transmission dip stick visible, please check the fluid level before you check the other areas.

please rate and god bless.

It sounds very much like your clutch is slipping. If the engine revs continue to rise when in gear and the car does not increase it's speed accordingly then if it is a manual car then you need a new clutch.

What car is this?
We suddenly experienced something similar in a Mercedes Diesel Auto and found the Turbo pipe was smashed/leaking like a sieve, so car went OK on level ground when not under torque but was a puffing billy with smoke trying to get uphill or anything like top speed on the motorway.
It it's an auto check the speed limiter hasn't been accidentally switched on.