First Timothy was written somewhere near the dose of the book of Acts around 62-63 A.D. Debate has raged over where the apostle Paul was when he wrote this letter, with some saying he was still in Rome and others some place else such as Macedonia or Laodicea. Just where Paul was or just when this letter was written does not make much difference, it's contents is what is important. Paul encouraged Timothy on how to conduct himself so has to bring honor to Christ and the name Christian. The letter also details what qualifications are necessary for men desiring to be elders and deacons. Plus he gives instructions on how to reprove those who are in need of reproving in such a way as to bring the desired results.
Second Timothy, many believe was the last letter that the apostle Paul wrote before his death at the hands of the Roman emperor Nero. around 68 A.D. Again Paul exhorts Timothy to continue strong in the faith even though Paul knows he is about to die. He admonished Timothy to study and to stay faithful in what he was teaching and preaching because there would soon be a time when some people would no longer be interested in the truth. He also encouraged Timothy to travel to Rome before the onset of winter, bring Paul's winter clothlng and books, especially the parchments.