Each deal is worth an annual average value of $3 million according to reports.
Filppula reunites for a third time with Steve Yzerman. The 35-year-old Finn played with Yzerman in Detroit and was signed by him in Tampa Bay.
Yzerman is in his first year as the Red Wings' general manager and he didn't waste any time adding a familiar player to his roster, making the move in the opening hours of free agency.
Filppula had 17 goals and 31 points last season with the New York Islanders. He has scored 185 times and has 494 points over 14 seasons with Detroit, Philadelphia the Lightning and the Islanders.
Nemeth, 27, has played with Dallas and Colorado in his six seasons. He had a goal and 10 points in 74 games for the Avs last season. In 2017-18 he had career highs with three goals and 12 points and was a plus-27.