B757-200
Flight Crew Air Transport Pilot (ATP)
Human-Machine Interface
Aircraft Equipment Problem Less Severe; Deviation - Altitude Crossing Restriction Not Met; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Overcame Equipment Problem
Aircraft
During descent on arrival. ATC became very backlogged and gave us a late descent from FL380 to FL350 putting us about 1000 ft high on profile. We had to ask for further descent below FL350 to stay on profile. We were switched to the next sector and given descent to FL240. The FO (First Officer) was flying and used speed brakes to get us on path again. We both recognized that the FO's VNAV path indicator showed on path and my indicator showed us 1000 ft high on profile; both FMAs (Flight Mode Annunciators) showed PATH and usually if the aircraft is off of path more than 400 ft the FMA with show VNAV speed and neither one did this. We were again given a late descent out of FL240 to descend via the arrival. When the FO set 6000 ft in the altitude window he pushed the altitude knob to start the descent and again had to use speed brakes to get down on profile. This time when joining the profile the FMAs and Path indicators all were correct however the aircraft descent rate shallowed out to 1000 fpm and the throttles kept advancing toward a higher setting even though the speed was approx 295 knots. The FO first mentioned that he thought the plane would be high on the ZZZZZ crossing. FO selected FLCH (Flight Level Change) and when he did; the magenta path indicator showed we were 5000 ft high and the throttles kept advancing. FO selected a lower form of automation and attempted to make the restriction. We were about 400 ft high at ZZZZZ and we stopped the descent at about 9700 ft to continue slowing from 275 knots to 250. The remainder of the flight the FO used FLCH and shut off autothrottles to control the continual advancing of the throttles beyond the commanded speed. After landing I made a very detailed write up concerning the VNAV anomalies.
B757 Captain reported that during descent the aircraft would not respond to automated inputs to stay on profile.