Charles Cawley notes that Konrad I was one of four children, brothers and a sister...
Considerable controversy surrounds the paternity of these children. Graf Konrad son of Gebhard (died 982) and Graf Udo son of Gebhard (died 949) have both been proposed as their father, Jackman being the principal proponent of the former theory while Hlavitschka has written extensively in support of the latter.... [E]ach has appeal and neither is obviously preferable. From a purely chronological point of view, the estimated birth date range of the daughter Judith does suggest more difficulty in sustaining the argument in favour of Graf Konrad being their father. The introduction of the name Heribert into the family suggests a strong family connection between these four siblings and the Vermandois family... [It] is suspected that the wives of Gebhard (died 949) and Udo son of Gebhard (also died 949) were daughters of Héribert I Comte de Vermandois. However, in neither case is it obvious that the four siblings ... were descended from these sisters. In the case of Gebhard, it appears difficult to identify his known son Konrad with Konrad who succeeded as duke of Swabia in 983, and ... it is chronologically hard to sustain that the siblings were the children of Gebhard's known son Konrad. In the case of Udo son of Gebhard, his known son Udo was recorded as bishop of Strasbourg so could not be the same person as Udo, one of the four siblings shown below, who was killed in 982. All these reservations suggest that there may be a completely different explanation for the parentage of these four siblings from the two theories of Jackman and Hlavitschka....
Thietmar names "Conradus Suevorum ductor…eiusdem frater Heribertus comes" when recording their deaths. "Otto…imperator augustus" granted property by the spurious charter dated 13 Jan 965 to the church of Oehningen, built according to the document by "domnus Chono comes de Oningen" with the consent of "uxoris sui Richlinde, filiorumque eius Eggeberti, Luipoldi, Chononis, Lutoldi", although ... this list of the couple's sons appears unreliable. The Chronicon Salernitanum records that "comes Alemannorum Saxonumque…Cono…Cuneus alius validus…missus" fought against the Greeks in southern Italy in [969]. Jackman suggests that this refers to the future Konrad I Duke of Swabia, on the basis that "Saxonumque" is added because of his supposed wife's Saxon origin, in addition using this reference to date the couple's marriage.
He succeeded in 983 as KONRAD I Duke of Swabia. Graf im Rheingau 985 and 995. Graf im Ufgau 987. Graf in der Ortenau 994.
The Annales Einsidlenses record the death in 997 of "Chuonradus dux" and the succession of "Herimannus filius eius in ducatum". The necrology of St Gall records the death "XIII Kal Sep" of "Chuonradi ducis Alamannorum". 1