The contents of the Gentile’s law are more difficult to pin down because very little revelation exists. From Romans, it appears that the contents are moral in nature. That is, the Gentiles knew the difference between right and wrong, between righteousness and evil. It also seems moral in nature because God is able to judge them according to it.
The question, then, is what is man’s responsibility during this time? It is simply this: to keep the law that is revealed, which is summarized by loving God and loving your neighbor. Jesus gives the synopsis of the law in Matthew 22. He states that all of the Law and the prophets (that is the entire Old Testament legal code) would never be broken if a man could perfectly love God and his fellow man. It is probably safe to assume that this same principle applies to Gentiles as well.
From this perspective, it also seems obvious that these two legal codes are not modes of salvation. Paul is quite clear that the Law did not save anyone. Also, no one could be saved by means of keeping the Law. The law was the rule of life in society and the regulations for worshiping the Lord.
The end of the dispensation of Law is somewhat ambiguous. Three options have been put forth, and each one has its merits. One of the difficulties in pinpointing the exact end is that the book of Acts describes a period of transition or at least a development in the understanding of the Apostles as to what exactly God was doing in the world. The three options for the end of the dispensation of the Law that dispensationalists have put forth are 1) the ministry of Christ, 2) the beginning of the Church, or 3) the destruction of Jerusalem in 70 A.D.
The first option is that in Christ’s life and death the Law was fulfilled or satisfied. The primary reason for this view is based on Paul’s teaching in Romans 10. Christ is said to have fulfilled the Law in his perfect life and sacrifice. The weakness to this view is that the Law itself and the dispensation of Law are being confused with one another. To say that Christ fulfilled the Mosaic law is not the same as saying that he brought the dispensation to an end.
The second option is that the beginning of the dispensation of the Church marks the end of the dispensation of Law. Similar to the end of the dispensation of human government which ended when the promise comes to Abram in Genesis 12, there is no climactic conclusion to the dispensation of Law given in Scripture. So, it could be that the same principle applies to the dispensation of Law and the Church.
The third option is that this dispensation ends with the destruction of Jerusalem in 70 A.D. On the basis of Hebrews 8, some see the dispensation of the law ending when Jerusalem was destroyed by the Romans. Hebrews 8 indicates that the Aaronic priesthood of the old covenant had not yet passed off the scene. This leads some to speculate that the temple was still standing and the priests were still officiating sacrifices at the Temple. Once the Temple is destroyed, the sacrificial system, which is part of the legal code, is also ended. It is possible, of course, for the Temple to exist after the dispensation has ended.