Narrative:

While leveling at FL320; EICAS 'right engine high stage' appeared. QRH procedure followed until step 4; when hi stage light extinguished. A short time later; the EICAS 'right engine high stage' reappeared. As the pilot monitoring completed the qhr procedure; which terminated with the right bleed and pack off; EICAS 'left engine high stage' appeared.knowing that we would become unpressurized shortly; we requested an immediate descent to 10;000 feet. We donned oxygen masks; established crew communication; and began the [urgent] descent. The QRH procedure of turning off the left engines bleed air valve and pack was complied with during the [urgent] descent. (The QRH did not address dual engine high stage indications. The QRH did not address using APU bleed air to supply the packs that were turned off per the QRH.) we were near zzzzz on the arrival with clearance to descend via the arrival when we began our [urgent] descent. ATC further cleared us direct ZZZ; then direct ZZZZZ1 for ILS xx. I had the pilot monitoring monitor the cabin altitude; which increased slowly and did not go higher than 10;000 feet. Once at 10;000 feet; we requested and were cleared to 9;000 feet in order to lower cabin altitude and be able to remove oxygen masks. We started the APU. I flew faster than 250 knots below 10;000 [feet] under captain's authority in order to reach ZZZ in minimal time. The approach was flown with normal procedures with delayed extension of final flaps and gear so as to keep engine thrust minimal since we were still indicating 'left engine high stage.' we discussed and notified ATC that we would clear the runway; shut down engines; and need to be tugged to parking. Arff [aircraft rescue and fire fighting] met us at the runway xx/taxiway. Thirty minutes after the engines were shut down; firefighters told us that their infrared flir device was showing that the left engine was the same temperature as our APU exhaust (which indicated +500C) and 'showed hot compared to the right engine.'it took over 40 minutes for the tug to arrive after tower called ZZZ operations. The tug arrived to [the] 'emergency aircraft' without a headset. This made communications with tower and arff difficult since we didn't know the tug driver's plan. [Between] taxiways; the tug lost power and started to veer to the left of centerline. I set the parking brake. The tug was smoking and arff assessed the situation. Again; having a headset to communicate with the tug driver would have been preferable in this situation with a hot engine and hot tug. A second tug was dispatched and we completed our 101 minute voyage to the gate. Maintenance logbook shows that both engines were changed at the end of [the previous month].

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Original NASA ASRS Text

Title: B767 flight crew reported EICAS messages appeared showing a 'R ENG HI STAGE' followed by 'L ENG HI STAGE'.

Narrative: While leveling at FL320; EICAS 'R ENG HIGH STAGE' appeared. QRH procedure followed until step 4; when HI STAGE light extinguished. A short time later; the EICAS 'R ENG HIGH STAGE' reappeared. As the Pilot Monitoring completed the QHR procedure; which terminated with the right bleed and pack off; EICAS 'L ENG HIGH STAGE' appeared.Knowing that we would become unpressurized shortly; we requested an immediate descent to 10;000 feet. We donned oxygen masks; established crew communication; and began the [urgent] descent. The QRH procedure of turning off the left engines bleed air valve and pack was complied with during the [urgent] descent. (The QRH did not address dual ENG HIGH STAGE indications. The QRH did not address using APU bleed air to supply the packs that were turned off per the QRH.) We were near ZZZZZ on the arrival with clearance to descend via the arrival when we began our [urgent] descent. ATC further cleared us direct ZZZ; then direct ZZZZZ1 for ILS XX. I had the Pilot Monitoring monitor the cabin altitude; which increased slowly and did not go higher than 10;000 feet. Once at 10;000 feet; we requested and were cleared to 9;000 feet in order to lower cabin altitude and be able to remove oxygen masks. We started the APU. I flew faster than 250 knots below 10;000 [feet] under Captain's authority in order to reach ZZZ in minimal time. The approach was flown with normal procedures with delayed extension of final flaps and gear so as to keep engine thrust minimal since we were still indicating 'L ENG HIGH STAGE.' We discussed and notified ATC that we would clear the runway; shut down engines; and need to be tugged to parking. ARFF [Aircraft Rescue and Fire Fighting] met us at the Runway XX/taxiway. Thirty minutes after the engines were shut down; firefighters told us that their Infrared FLIR device was showing that the left engine was the same temperature as our APU exhaust (which indicated +500C) and 'showed hot compared to the right engine.'It took over 40 minutes for the tug to arrive after Tower called ZZZ Operations. The tug arrived to [the] 'Emergency Aircraft' without a headset. This made communications with Tower and ARFF difficult since we didn't know the tug driver's plan. [Between] taxiways; the tug lost power and started to veer to the left of centerline. I set the parking brake. The tug was smoking and ARFF assessed the situation. Again; having a headset to communicate with the tug driver would have been preferable in this situation with a hot engine and hot tug. A second tug was dispatched and we completed our 101 minute voyage to the gate. Maintenance logbook shows that both engines were changed at the end of [the previous month].

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.