Contractors started their operations on Monday and have so far successfully retrieved several parts of the structures, which were washed away last October.
Annandale South Councillor Sean Marshall yesterday said everything is on schedule and work is progressing well.
He confirmed the first bridge has been removed this week and the second one will be taken away next week.
Meanwhile, drone operator Jamie Grant has been following proceedings from the skies and posting updates on Facebook, via the Annan Tale of Two Bridges group.
Once removed, the bridge remains will be stored at Annan Cemetery.
Explaining why a bridges group spokesperson said: “The cemetery is the nearest council-owned piece of land we can use for (free) storage. “The Cuthbertson was a listed War Memorial, so parts of it will need to be salvaged. It was agreed that it could be kept there so that volunteers from our group could use parts to create memorial benches. This will be done in their own time and expense.
“We are very grateful to the Council for funding both the salvage operation and also employing someone specifically to investigate all options regarding new bridges. A full, public consultation will be made before any decisions are made.”