The deuteron NMR lineshapes in the tilted antiferroeelectric smectic liquid crystalline phases are evaluated for: i) the case of a discrete short pitch modulation P1 = N • d where N = 2,3,4, ii) for a superposition of two modulations p1 and p0 where p0 ≫p1 as well as iii) for the case where in addition rapid molecular exchange between adjacent layers takes place due to translational diffusion. The results are compared with the experimental deuteron NMR spectra of α-CD2 deuterated MHPOBC in the Sm C*A phase measured at different angles between the magnetic field direction and the normals to the smectic layers. The alternating tilt structure of the Sm C*A phase is confirmed