Marilyn Smith, 56, from Gwynedd, was last seen in her hometown of Bangor on July 28.
Marilyn is described as being Afro Caribbean with black coloured hair.
Inspector Douglas Hughes, of North Wales Police, said: “Initially we believed that she may have booked into a B&B in the Bangor area, however following our enquires carried out so far we believe she may have travelled to the Powys area. She also has connections to the Nottinghamshire area.
“I would urge anybody who may have information, or anybody who may have seen Marilyn to contact us. Equally I am appealing direct to Marilyn to make contact with us to let us know she is safe and well.”
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Anybody who may have seen Marilyn or have information on this matter, is asked to contact North Wales Police on 101 quoting reference number 13668.
Alternatively contact the Control Room direct via the new live web chat service http://www.north-wales.police.uk/contact/chat-support.aspx