Main (alpha-) and secondary (beta-) relaxation of the linear poly(ethylene-alt-propylene) (PEP) with different molar masses are investigated by dielectric and H-2 NMR spectroscopy. Regarding the alpha-process, time constants in the range 10(-11)-1 s are reported, and the correlation function is described by a Cole-Davidson function with stretching parameter beta congruent to 0.34. Both methods show clear evidence of a pronounced beta-process; the latter is thoroughly studied by different NMR techniques. The results are compared to toluene-d(3) and toluene-d(5), respectively, as reference systems. The solid-echo spectra as well as the spin-lattice relaxation display typical features of spatially highly restricted angular displacements similar to those reported in other glass formers showing a beta-process-like toluene. Above T-g all chain segments participate. As both chain and methyl group were deuterated and as the fl-process is rather fast, its angular displacement growing with temperature above T-g is directly reflected in a reduction of the effective quadrupolar coupling constant; i.e., the H-2 solid-state spectra get narrower upon heating. Although the time constant tau(beta) is the same for both segments, the angular amplitude of the methyl group bearing segment is larger than that of the other chain segments, and alpha- and beta-process merge at high temperatures. For the other segments a merging appears not to happen. In this sense, the beta-process is anisotropic as is demonstrated also for toluene-d(3) for which it essentially involves a rattling around the C-2-axis-a finding, however, which does not explain the fact that the fi-process is dielectrically active. Regarding PEP below T-g, there are indications that only about half of the methyl group bearing segments are involved in the beta-process whereas the other segments fully participate. Finally, we discuss possible implications of our findings regarding the nature of the beta-process and compare time constants tau(beta)(T) as well as tau(alpha)(T) of polymers like poly(methyl methacrylate), poly(propylene glycol), and poly(isoprene) among others.