A Status Yellow Wind and Rain warning is affecting counties in the northwest, west and south.
Cavan, Leitrim, Donegal, Mayo and Sligo are advised to be alert for heavy rainfall.
Clare, Cork, Kerry, Limerick, Donegal and Connacht are warned of high winds.
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And a Status Yellow wind warning is due to come into effect at 11am for Leinster, Cavan, Monaghan, Tipperary and Waterford, with severe gusts expected.
It will be in place until 9am on Monday.
Met Éireann's Paul Downes says temperatures could dip as the week goes on.