An investigation of the orbital period changes of the neglected eclipsing binaries, RY Aqr, SZ Her, RV Lyr and V913 Oph, is presented based on all published minima times. Although the explanation of magnetic activity on the surface of the secondaries of the studied Algols is still open, the preferred light-time effect due to the unseen components around the systems seems more plausible in explaining the tilted sinusoidal variations with relatively high-amplitudes. The minimal mass values of possible tertiary components have been estimated to be about 1.06, 0.25, 0.78 and 2.85 M(circle dot) for RY Aqr, SZ Her, RV Lyr and V913 Oph, respectively and the results indicate that their contributions to the total light of the eclipsing pairs are measurable with high accuracy photometric and spectroscopic data, if they exist. Applegate's (1992) model has been discussed as an alternative mechanism assuming that the cooler components have magnetic cycles. It is found that the model parameters of RY Aqr and V913 Oph are consistent with the required values in Applegate's model. In addition to the first detailed orbital study on these systems, a statistical survey on the character of the O-C variations of classical Algols has revealed that about 50 percent of the systems show cyclic behavior. This means that the presence of possible third bodies around classical Algols should be tested with careful analysis using new data. (c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.