(CNN) US pilots who fly the Boeing 737 Max have registered complaints about the way the jet has performed in flight, according to a federal database accessed by CNN.

In one of the complaints, a captain reported an autopilot anomaly which led to a brief nose-down situation -- where the front of the aircraft pointed down, according to the federal database. In another complaint, a first officer reported that the aircraft pitched nose down after the autopilot was engaged during departure. The autopilot was then disconnected and flight continued to its destination, according to the database.

Although the data doesn't identify the pilots or their airlines, two US carriers fly the 737 Max 8: American Airlines and Southwest.

Extraordinary worldwide attention has been focused on the jet -- Boeing's biggest-selling airliner -- after Sunday's crash of a new Ethiopian Airlines 737 Max 8, minutes after takeoff from Addis Ababa, which killed all 157 people on board. Ethiopian Airlines Flight 302 was the second deadly crash of the same new plane type within five months. The crash of Lion Air Flight 610 shortly after takeoff from Jakarta last October killed all 189 people on board.