Boeing is being sued by more than 400 pilots who flew its 737 Max plane, in a class-action lawsuit that accuses the manufacturer of an "unprecedented cover-up" of issues with the aircraft.

The pilots claim in the lawsuit that the 737 Max's design gave it "inherently dangerous" defects when pilots tried to fly it, the Australian Broadcasting Corporation reported.

They also say they have suffered financial damage as the plane remains grounded around the world, and have experienced career uncertainty as a result.

The pilots join a slew of other groups affected by 737 Max crisis, including airline pilots, airlines, and victims' families in looking for damages from Boeing after the two deadly crashes involving the Max.

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More than 400 Boeing 737 Max pilots are suing the company over what they allege was an "unprecedented cover-up" of "known design flaws" in the plane, and over the financial losses they face as the plane remains grounded after two fatal crashes.

A class-action lawsuit was filed against Boeing on Friday "for financial and other losses arising from the circumstances and grounding of the MAX fleet," according to the two law firms representing the pilots, based in Chicago and Australia.

While they said that they could not yet calculate the size of pilots' losses, they "are expected to be in the millions of dollars," the law firms said.

Colleagues of victims of the crashed Boeing 737 Max Lion Air flight throw flowers off a boat at the site of the crash in November 2018. Ulet Ifansasti/Getty Images

The 737 Max has been grounded around the world since March, after a second fatal crash involving the plane killed 157 people in Ethiopia. The first crash in Indonesia in October 2018 killed 189 people.

Read more: Here are all the investigations and lawsuits that Boeing and the FAA are facing after the 737 Max crashes killed almost 350 people

The law firms said that this "adversely affected" pilots' income and gave them career uncertainty, and that they were filing the lawsuit during the Paris Air Show "to send a message to Boeing that its desire for aircraft sales must never again impact on aviation safety."

In the court documents, the pilots allege that Boeing "engaged in an unprecedented cover-up of the known design flaws of the MAX, which predictably resulted in the crashes of two MAX aircraft and subsequent grounding of all MAX aircraft worldwide," according to the Australian Broadcasting Corporation (ABC).

The suit says that the pilots "continue to suffer significant lost wages, among other economic and non-economic damages" since the fleet's global grounding.

Boeing declined to comment when contacted by ABC, and did not immediately respond to a request for comment from Business Insider.

The cockpit of a Boeing 737 Max plane. Ted S. Warren/Associated Press

The first pilot to file the suit, referred to as "Pilot X," claimed that the plane's automated anti-stall software, called MCAS, gave the plane "inherently dangerous aerodynamic handling defects."

Pilot X is identified as a Canadian citizen and a 737 Max pilot, but according to the ABC has remained anonymous for "fear of reprisal from Boeing and discrimination from Boeing customers."

The other pilots are described as being from a "major international airline," according to ABC.

Pilot X also criticized Boeing for designing the MCAS system to rely on just one sensor, claiming that the "effective design causes the MCAS to activate based on the single input of a failed [angle of attack] sensor without cross-checking its data with another properly functioning AOA sensor."

Read more: Boeing is in talks to settle with families suing it over 737 Max crash deaths and avoid a potentially excruciating trial

This MCAS was highlighted in preliminary reports into both crashes, which found that the pilots could not control it after the plane recorded erroneous AOA readings.

Boeing maintains that the design of plane is safe, though it promises that an upcoming software update will make it "one of the safest airplanes ever to fly" when it is certified to fly again. The update will see the MCAS system work with data from two sensors.

Boeing Commercial Airplanes CEO Kevin McAllister and International Airlines Group CEO Willie Walsh announce IAG's intent to buy 200 737 Max planes at the 2019 Paris Air Show. REUTERS/Pascal Rossignol/File Photo

Boeing executives told reporters at the Paris Air Show that the plane's design, including relying on one sensor, met all regulatory requirements.

Pilot X also criticized Boeing's communication with pilots, saying that Boeing "decided not to tell MAX pilots about the MCAS or to require MAX pilots to undergo any MCAS training" so that its airlines could start running "revenue-generating routes as quickly as possible."

Boeing was also previously criticized by the American Airlines pilots, who chastised company executives in November, after the first crash, for not telling them about the MCAS system.

"These guys didn't even know the damn system was on the airplane, nor did anybody else," one pilot told Boeing executives.

Read more: Behind Boeing's offer to settle with victims' families in a 737 Max crash is a hardball legal strategy that could leave them with nothing

Other pilots have also come forward to seek money from Boeing over the grounded jets as uncertainty remains over when the US Federal Aviation Administration will certify the update and allow the 737 Max to fly again.

A number of grounded Southwest Airlines Boeing 737 MAX 8 aircraft are shown parked at Victorville Airport in Victorville, California. Reuters

Southwest Airlines' pilots union will seek compensation from Boeing, CNBC reported, over lost wages and legal costs for complying with the Department of Justice's investigation.

The Department of Justice investigation into how the plane was certify to fly is one of a number of federal and Congressional investigations into the plane and how the FAA gave it the green light.

Boeing also faces a slew of lawsuits from families of victims around the world, and faces a growing number of airlines demanding compensation from Boeing as they cancel flights over the grounded plane and face delays to the deliveries of more planes.

Pilot X is also making an out-of-court claim against the FAA, the law firms said, and they will "file a lawsuit against the United States for the FAA's negligence in certifying the MAX by Christmas Eve of 2019" if that response is inadequate.