A Yellow Weather Warning has been issued by Met Eireann.
Forecasters are predicting a band of heavy rain falling I n southern counties on Sunday night, which will extend northwards overnight and during Monday.
The experts say the rain will turn wintry with falls of sleet and snow in some areas.
The Weather Warning is valid from 6pm on Sunday to Monday at 6pm.
Meanwhile tonight will be cold, with frost and a risk of icy patches, especially away from coasts.
Minimum temperatures will range from -2 to +2 degrees.
Irish Weather Online experts said the cool, wet and unseasonable weather will likely continue with more rain, sleet or wet snow towards the end of the week.
But then the second week of April still gives some promise of warmer weather eventually with highs possibly returning to more normal values in the mid-teens.
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