It's over recent Census results, which showed a decline in the number of Welsh speakers.
The Welsh Government say the building remains open to staff and visitors as usual.
Cymdeithas are holding a peaceful protest at one of the entrances at the Welsh Government offices in Cardiff. The main reception remains open as usual to all staff and visitors.
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Rail users in Wales could be hit by disruption later this week after talks to avert a 48-hour strike broke down.
Prince Charles was all smiles during his visit to Cardiff today meeting cricketers and enjoying a chat over a cup of tea.
The Prince of Wales met members of the England and Australia cricket teams ahead of the Ashes tournament which starts on Wednesday.