It's understood a leading figure in the Republican movement was arrested, as officers carried out more than 20 searches in Louth, Wexford and Dublin.
The four men are being held over alleged offences including directing terrorism, membership of an unlawful organisation, and possession of explosives.
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Bomb disposal experts spent several hours decommissioning devices in a number of locations yesterday.
Conor Feehan of the Herald newspaper says Gardai may have prevented a serious attack during the visit of Prince Charles.