Nuclear magnetic relaxation times T2, T1, and T1ρ are reported for natural rubber, polybutene-1, polyethylene, polyvinyl chloride, polychlorotrifluoroethylene, polyethylene terephthalate and polycarbonate. The measurements cover the temperature range form 77 K to above the melting or glass transition regions. All seven polymers exhibit glass transition effects. Methyl group reorientations are observed at low temperatures. An additional ethyl side group motion and a crystalline rotator phase (>50°) are observed in polybutene-1. Other mechanisms are discussed. Good agreement is found between mechanical, dielectric and n.m.r relaxation frequencies.