From "Debrett's Kings and Queens of Britain" by David Williamson, ISBN 0-86350-101-X, p. 43:
No children by his first wife. He married his mistress, the mother of all his children, after the death of his first wife.

After the murder of his father in 942, Normandy was given over to warfare between rival Viking bands, and during the early reign of Richard I, the chief supporter of settled order appears to have been not the duke but the French king, Louis d'Outre-Mer. Terrible wars ravaged the province of Normandy from 961-965. In 965 Duke Richard I made a pact with King Lothair of France at Gisors to settle the war. Scandinavian influence remained strong in Normandy, and King Ethelred II of England protested that Viking raiders of England were receiving hospitality and assistance in the Norman ports in the closing decades of the tenth century.120

In a charter given to Fécamp in 990 Richard I styled himself 'count and consul'. Other titles were used alongside this, and with the advance of the eleventh century that of 'duke' came to predominate. By acquiring the traditional title of count, the Viking dynasty not only vested itself with the sanctions of legitimacy, but it could lay claims to important privileges and powers, for example wide rights to the profits of public justice, and fiscal rights over imperial estates which lay within his jurisdiction.120

Weis' "Ancestral Roots. . ." (39:22), (119:24), (121E:20), (177:3), (214:22), (235:19), (250:20). "RICHARD I, "the Fearless", Duke of Normandy, b. Fecamp ca. 933, named father's h. 29 May 942, d. 20 Nov. 996; m. (1) (Danish wife) GUNNOR, d. 1027 or 1031, dau. of the forester of Arques, but betrothed ca. 945 & event. m. (2) 960 to Emma, d. ca. 968, dau. HUGH CAPET ..., Count of Paris. After Emma's death, m. (Christian marriage) GUNNOR to legit. their children. "

Cokayne's "Complete Peerage" (Appendix D to v.VII, p.711), identifies him as father of ROBERT, COUNT OF EVREUX. Stuart's "Royalty For Commoners" (166:33).

From Rosamond McKitterick.s, "The Frankish Kingdoms under the Carolingians 751-987", London & NY (Longman) 1983, pp. 238-239:
"When in 942 WILLIAM was murdered at the instigation of COUNT ARNULF OF FLANDERS, his son Richard, still a minor, succeeded him. LOUIS IV and HUGH THE GREAT each tried to seize Normandy, and LOUIS took charge of Richard. He then ensconced himself at Rouen and HUGH took Bayeux, which still had a Scandinavian leader called Sitric. Richard escaped from his custody at Laon, retook Rouen, and called on another Viking leader, Harald of the Bassin, for help.
The Normans under Richard were able to re-establish their autonomy and from 947 Richard governed in relative peace. In 965
he swore allegiance to the Carolingian king Lothar [son of LOUIS IV] at Gisors. Richard's official marriage was to Emma, daughter of HUGH THE GREAT; they had no children, but by his common-law wife GUNNOR, a Dane, he had many. RICHARD II, son of GUNNOR and Richard I, succeeded his father in 996, another son Robert was archbishop of Rouen from 989 to 1037 and EMMA their daughter became queen of England on her marriage to AETHELREAD, a position she maintained after his death in 1016 by marrying Knut. GUNNOR's nephews and other relatives furthermore formed the core of the new aristocracy which developed in the course of the eleventh century. Unfortunately we know little about the internal organization and history of Normandy until the reign of RICHARD II."

From "Predatory Kinship and the Creation of Norman Power, 840-1066" by Eleanor Searle, University of California Press, 1988:
"The Acknowledged Children of Richard I: Sons. The most revealing evidence of the prestige and power of Richard and his successor is to be found in the endowments and marriages of their children. The wife whose Norseness and high status made her an acceptable equal in the eyes of his chieftains was a woman whose children commanded paternal recognition, for they would have powerful maternal kinsmen upon whose loyalty they could call. Even so, it is remarkable that Dudo, with GUNNOR at his side, tells the reader only the number of children she bore Richard: five boys and three girls. He does not give their names, and Richard's sons defy full identification.
RICHARD II was certainly GUNNOR's son, as was his virtual co-ruler, Robert, archbishop of Rouen. Charters identify their relationship clearly, but they do not identify any of her husband's other sons as GUNNOR's...." (p. 132, see below for source) "Richard I and his new settler-in-laws of the 960s were the winners who lasted. In becoming so they learned (and taught) two principles of success that marked them off from the Franks. They learned the value of a strong centralizing chieftain who could at least freeze the status quo once his own local chieftains had taken what they wanted. The more successful he was, the more chiefs attached themselves to him for just this: with his warranty, backed by his chieftains, their defeated enemies could not recover by violence what had been taken from them by violence.
Thus were the Norman dukes 'settlers of quarrels.' Fearlessness was the necessary quality in such a coordinating chieftain, and Richard I, who has no encomiast of his deeds, has at least this sobriquet, "the Fearless.” Those who were great fighters and the ruthlessly, selectively violent, were the great centralizers among the threatened and rapacious Norse."
During the minority of his (WILLIAM LONG-SWORD) successor, Duke Richard, KING LOUIS IV, who was making an expedition into Normandy, was captured by the inhabitants of Rouen and handed over to HUGH THE GREAT. From this time onwards the dukes of Normandy began to enter into relations with the dukes of France; and in 958 Duke Richard married HUGH THE GREAT's daughter. He died in 996. (Succeeded by RICHARD II.)

He fought a long and bloody war with rival Viking bands to retain his inheritance.