Since Jesus' death and resurrection occurred approximately in the year A.D 33, these two gospels were written during the time when eyewitnesses, both friendly and unfriendly, were still alive.
Each of the first three Gospels contains predictions by Jesus concerning the destruction of Jerusalem and the Temple (Matthew 24; Mark 13; Luke 21), but none records the fulfillment. Hence, the composition of the first three Gospels most likely occurred sometime before this event, otherwise their destruction would have been recorded.Boldly and without hindrance he preached the kingdom of God and taught about the Lord Jesus Christ (Acts -31). Since we know that the gospel of Luke was written before the Book of Acts, we can then date the Gospel of Luke sometime around A. Paul wrote of a brother who was well-known among the churches for the gospel.The inference is that Acts was written while Paul was still alive, seeing his death is not recorded. There is ancient testimony that this refers to Luke and his written gospel.The evidence shows that the four Gospels were written in a relatively short time after the death and resurrection of Jesus Christ.Examining the internal evidence of the New Testament itself can make this plain.