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Scottish-born Lithgow grew up in Invercargill before moving to Tasmania in 1894 where he wrote the march in 1901 in tribute to his former home town.
The Invercargill March became popular at Gallipoli and that popularity has extended around the world, especially in the US where it is reportedly a top favourite with the US Marines.
It is a standard among brass bands worldwide.
Descendants of Lithgow came from Australia to attend the unveiling on Saturday.