The Minister for Justice, Mr O'Donoghue, and the Garda Commissioner, Mr Pat Byrne, are visiting gardai serving on peacekeeping operations in former Yugoslavia and Cyprus.
Forty-five gardai are serving in parts of Bosnia and eastern Slovonia which saw some of the worst violence of the civil war in the region.
The two men yesterday attended a ceremony where the 10-strong Garda contingent serving in the eastern Slovonia region of Croatia were presented with United Nations peacekeeping medals.
On Monday Mr O'Donoghue and Mr Byrne met the 35 gardai serving in Bosnia-Herzegovina.
Later today the party will fly to Cyprus where another contingent of 15 gardai is also serving with the United Nations.
Gardai have been serving in former Yugoslavia since April 1992. One officer, Sgt Paul Reid (39), who was married with three children, and from Letterkenny, Co Donegal, was killed when his car was hit by shrapnel and crashed in "Snipers' Alley" in central Sarajevo in May 1995.
The gardai in former Yugoslavia are serving with the United Nations, but the policing element of the UN peacekeeping operation is to be taken over by the Organisation for Security and Co-operation in Europe (OSCE).
Details of the hand-over of administrative duties are still emerging, and it is expected that during his visit Mr O'Donoghue will announce what the Government's intentions are concerning the role the Garda Siochana will play in the new OSCE police force.