There are two basic models used to explain the origin of the Gospel accounts of Jesus' life. The first model is that the Gospel stories arose out of the collective memory of the Christian community. Under this model, it is argued that the Gospel stories circulated in the Christian community, creating a kind of "Jesus tradition," which was later encapsulated by the Gospel writers, probably at a time when all the original eyewitnesses had died.
However, the evidence does not support this model. It is much more likely that the four Gospel accounts were more directly linked to specific eyewitness accounts of the events described.
The case for the Gospels representing eyewitness testimony has been made most recently by Richard Bauckham, Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony (Grand Rapids: Eerdmans, 2006). This work sets a new standard in the analysis of the Gospel accounts. Written from a scholarly evangelical perspective, it evaluates the evidence supporting the argument that the Gospels were written from eyewitness accounts.
This case begins with the argument that Papias, a Christian writer from the early second century AD (from Hierapolis in the old Roman province of Asia), said that he had been told that Matthew had written down a book of Sayings of Jesus in the Hebrew dialect (that is, in the Aramaic language spoken in Palestine), "but each person interpreted them as best he could." Matthew's Book of Jesus' Sayings stands in place of the mysterious Q source that scholars have been seeking to find (by textual analysis of Matthew, Luke and the Gospel of Thomas) for the last one hundred years.
Papias also indicated that Mark was the interpreter of Peter, and that Mark's purpose in writing his Gospel was to faithfully reproduce the substance of what Peter said about Jesus' life and words.
Matthew's Gospel was not itself an eyewitness account, but it was based upon two eyewitness accounts. It appears to have been an edited work, being constructed from Matthew's Book of Jesus' Sayings and from Mark's Gospel. There is no doubt about the influence of Mark's Gospel upon the Gospel of Matthew, since most of Mark's Gospel is reproduced in Matthew. The Markan elements in the Gospel of Matthew are found in the same order as they are found in Mark, with some measure of summarising of the material having been carried out by the "Matthean editor."
It can be argued that most of Matthew and Mark were based on eyewitness accounts. This increases our confidence that they are likely to represent substantially what the two observers at first hand, Matthew and Peter, believed to be a fair testimony to Jesus' life and words.
The situation with the Gospel of Luke is slightly different. The author, most probably Luke, indicated that he approached the matter as a historian would have done, collecting as much evidence as he could from the available sources. A study of the text of Luke indicates that the two main sources for the Gospel of Luke were the book of Matthew's Book of Jesus' Sayings and the Gospel of Mark. However, Luke was not limited to these sources, but referred to other accounts as well, which in turn were based on eyewitness accounts. Since it appears that Luke spent time in Palestine during Paul's imprisonment in Palestinian Caesarea (ca. AD 60), it is likely that he collected his sources for his gospel at that time, and that he wrote his two works, the Gospel of Luke and the Acts of the Apostles, when he was in Rome, again accompanying Paul.
Traditionally, the Gospel of John has been attributed to John, the son of Zebedee, one of Jesus' twelve disciples. However, the Gospel of John does not positively identify the author, but rather the author calls himself the "Disciple Jesus loved." It is unlikely that this disciple was the John who was the son of Zebedee, since the Beloved Disciple had a home in Jerusalem (to which he took Jesus' mother after the crucifixion). He is also likely to have been the unnamed disciple who met Jesus with Andrew (John 1:35-42), and the unnamed disciple who went into the high priest's house (John 18:15), and one of the two unnamed disciples who met Jesus at Lake Tiberius (John 21:1-2). Since the fisherman son of Zebedee is unlikely to have had a home in Jerusalem (in addition to his home in Galilee), and to have known the high priest, and to have the facility in Greek and Greek philosophy evident in the Gospel of John, one should abandon the traditional ascription of this work to the John, the son of Zebedee, and instead look for another man named John, who was also a disciple of Jesus.
The work itself supports this argument, since it includes elements, such as Jesus' dialogue with Nicodemus, that indicate the author's access to the higher levels of Judean society, beyond that found in the other three Gospels. The work itself is suggestive of an author who moved in the same circles as Nicodemus.
This brief analysis serves to show that a reasonable argument can be made that all four Gospels were based upon eyewitness testimony, with the fourth Gospel being written in its entirety by an eyewitness.