It emerged in court that police discovered parts of a bomb in a locker at National University of Ireland, Maynooth, as part of their investigation.
The men aged 59, 23 and 22 are from counties Tipperary, Louth and Dublin.
They have been remanded in custody.
Dylan Cahill, 22, of Lower Irishtown, Clonmel, County Tipperary, was charged with IRA membership and possession of a semi-automatic pistol, four rounds of ammunition and two pipe bombs at Glenfarne, County Leitrim, on 13 May.
He was remanded in custody until 9 June with liberty to apply for bail.  RTÉ reports that his case will be mentioned this Tuesday.
Seamus McGrane, 59, of Little Road, Dromiskin, County Louth, was charged with IRA membership on dates between 23 December 2009 and 13 May 2015 and directing IRA activities on the same dates.
He was remanded in custody until Wednesday, 20 May.
Donal Ó Coisdealbha, 23, of Abbeyfield, Killester, County Dublin, was charged with IRA membership and with having possession, in a personal storage locker under his control at National University of Ireland (NUI), Maynooth, a component part for an explosive device, described as a timing and power unit.
He was also remanded in custody until Wednesday, 20 May.
Three other men arrested in connection with the investigation have been released from police custody without charge.
Files are being prepared for the Republic of Ireland's Department of Public Prosecution.
The charges follow a police operation earlier this week in counties Wexford, Dublin, Leitrim and Louth.
Three men have appeared before the Special Criminal Court in Dublin charged with membership of the IRA and other offences.