The Chronicle of Alberic de Trois-Fontaines names "comitis Conradis" as son of "Gislebertus comes de Luscelenburch".
Vogt of St Maximin at Trier and of Stablo. He succeeded his father in [1056/59] as Comte [de Luxembourg]. He captured Eberhard Archbishop of Trier, for which he was excommunicated. "Conradus comes" founded the Benedictine abbey of Münster [Altmünster] in Luxembourg, with the consent of "uxore mea Clementia cum filiis et filiabus nostris", by charter dated 7 Jul 1083.
He died while on the pilgrimage which had been required before his excommunication could be lifted. He is referred to as "Comes de Luccilinburg" on the seals of Münster abbey, the first of his family to which this title was ascribed. The Chronicon of Bernold records the death in 1086 of "Chonradus comes, frater Heremanni regis" while on pilgrimage to Jerusalem. His tomb at Münster records the death of “comes Conradus...peregrinus sepultus in terra decenter non sua...VI Id Aug” 1086, the return of his body four years later, and its burial in the presence of “conjuge sua Clementia, per manum Adalberonis primicerii Metensis, Henrici comitis, Conrardique comitis...Rodolpho abbate filio comitis”. 1