The SES issued flood and watch warnings on Sunday for both dams, one at Basket Range and the other at Hope Forest, both in the Adelaide Hills.
A small number of property owners who could be impacted by the dam failures have been door knocked by SES personnel and informed of the situation.
On Sunday night, the SES warned residents they should only leave if they are sure the path out is safe and clear.
"There is a high risk of a dam failure in Hope Forest which may effect properties near the intersection of Bevan Road, Phillips Road and Verrall Road, as well as, in the vicinity of Brookman and Decaux Roads which may threaten you and your family's safety," the SES said in a statement.
"Road closures remain in place for Bevan Road, Verrall Road, Phillips Road, Brookman Road and Decaux Road."
A similar warning was also put out for residents in Basket Range.
"There is a risk of a dam failure in Basket Range which may threaten you and your family's safety. Low lying properties may be impacted on Lobethal Road along Deep Creek towards Knotts Hill Road," the warning said.
"Road closures are in place.The risk has reduced for properties along Deep Creek from Lobethal Road towards Elborough Avenue. Dewatering of the dam will continue overnight and may cause water and debris in the waterways and across roads within the warning area."
Residents are also being urged to monitor weather conditions and warnings, follow emergency plans and prepare for flooding.
SES chief of staff Derren Halleday said both dams have been inspected by structural engineers to gauge their integrity.
"As well as the engineer reports, we have personnel physically on-site monitoring and inspecting the dams and their immediate surrounds and we are also working closely with the Department for Environment and Water,'' he said.
"Highly trained SES remotely piloted aircraft personnel have captured drone footage of the dams which will greatly assist us in determining the best way forward.''
He said continual rain in the past few days had raised the risk profile of both dams.
As a result three residents, two from Hope Forest and one from Basket Range, have voluntarily relocated, Mr Halleday said.
The weather warnings are expected to stay in place as a series of troughs associated with a slow moving, deep low pressure system to the south of the state move across the central parts.
The Bureau of Meteorology has severe weather warnings in place for parts of South Australia, with a 102km/h wind gust recorded at Murray Bridge on Saturday evening.
The warning said winds up to 100km/h over the Mount Lofty Ranges would ease on Sunday afternoon, but the risk of falling trees is high after recent heavy rain.
The BOM said on Sunday morning other locations which could be affected by damaging winds included Mount Barker, Murray Bridge, Victor Harbor, Strathalbyn and Mannum.
"Damaging wind gusts are expected to ease below warning thresholds during Sunday afternoon," the alert stated.
The bureau also issued flood warnings for parts of the North West and North East Pastoral Districts ahead of more rain lashing South Australia.
Showers and increasing rain are forecast to develop from Monday, with flooding possible from Tuesday.
The bureau warned communities may be cut off with roads and transport being affected.
For SES assistance phone 132 500 and if the matter is life threatening call triple-zero.
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