SYDNEY—The hunt for the remains of Malaysia Airlines Flight 370 is falling behind schedule as the lead contractor, an oil and gas firm with little experience in searching for deep-sea wreckage, battles issues with its equipment and bad weather.

Fugro NV has struggled to acquire and fit its ships with sonar capable of operating at extreme depths in a remote part of the southern Indian Ocean, where investigators believe the plane went down last March with 239 people on board.

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