Classical Cepheids are a cornerstone class of pulsators, fundamental to testing stellar evolution and pulsation theories. Their secular period changes, characterized through O − C (Observed minus Calculated) diagrams, offer valuable insights into their evolution. While evolutionary period changes are well understood from both observational and theoretical perspectives, shorter timescale period changes (on the order of (∼ 102-104 days) - known as non-evolutionary period changes are yet to be systematically explored. In this work, we present a detailed and comprehensive search for non-evolutionary period changes using O − C analysis of Magellanic Cloud (MC) Cepheids, based on 20+ years of OGLE photometry data. Our sample includes both the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) Cepheids, focusing on single radial mode Cepheids (both fundamental (FU) and first overtone (FO) modes). The results are grouped into two phenomena: (a) Cepheids in binary systems (b) Non-linear period changes.