A delicate operation to remove a crane that fell on a Wolli Creek apartment block has begun but residents have been told to expect further delays, leaving them homeless for at least another night.

The 30-metre crane fell onto the 10-storey building in Sydney's inner south last Sunday, crashing into the penthouse apartment and leaving three workers in need of rescue.

About 200 residents who had to be evacuated have spent a week moving from hotel room to hotel room.

On Saturday morning, the cabin and the horizontal arm of the crane were removed by larger cranes, exposing the damage caused when the arm hit the top of the building last weekend.