Red giant stars located on the AGB are intrinsically variable, which is usually associated with stellar pulsation. The complex light variation of semiregular variables (SRVs) has many alternative explanations. Besides the pulsation, other contributors to variability cannot be solidly excluded, such as time-dependent surface inhomogeneities, ellipsoidal deformation due to the presence of a close companion, or spots on a rotating star. The identification of ultra-short period M-giants with periods of a few days raised the possibility of very high-order overtone pulsation of these stars. Thus, it is very important to draw various constraints on the stellar pulsation in semiregular variables and to separate other physical causes. Here we present new empirical evidence for radial pulsation in SRVs through studying their period-gravity relation, following the ideas outlined by Fernie (1995, F95). F95 studied a log P versus log g relation for various types of radially pulsating variable stars. He found a well-defined linear relation, which might serve to test whether the pulsation is radial or nonradial and, in the former case, fundamental or overtone. The main goal of our study is to extend the relation into the domain of SRVs.