Christopher, 12, and Steven Gallacher, 11, were last seen in the city centre at about 2pm on Saturday.
Christopher is 5ft 5in with dark brown hair, and he was wearing a bright yellow hooded jumper and shorts.
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His younger brother is about the same height and has dark brown hair in a mohawk style, with patterns shaved into the sides. He was wearing a light coloured T-shirt, green jogging bottoms, glasses and was carrying a backpack.
Officers from Police Scotland are searching the city centre area for the youngsters, and anyone who has seen them or knows of their whereabouts is urged to contact 101.