Crews have been in other parts of the town filming Secret Invasion since the beginning of last week.
Dozens of people are busy carrying set and filming equipment into the historic building, a huge light has been positioned over The Piece Hall and there are lots of trucks and other vehicles parked up.
A crowd of extras has been seen gathering outside one of the entrances including some in what looked like traditional Russian costumes.
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The car park at Eureka! is also busy with movie trailers, catering van and other vehicles.
There has been no sign of any of the stars, including Samuel L Jackson, yet.
The Piece Hall is shut until Tuesday, February 1, while filming takes place. Eureka is also closed, until Friday.