In the present article, we analyze long-term changes in the intensity of galactic cosmic rays (GCRs) in different polarity epochs of the solar magnetic cycles from 1959 to 2014. Our purpose is to carry out a study of the delay time (DT) between the changes of the GCR intensity and various parameters characterizing the conditions in the heliosphere. We prove the existence of varying DTs between the changes of GCR intensity and the parameters characterizing solar activity, such as sunspot number and tilt angle. Based on our investigation, we obtained different DTs in epochs with different global solar magnetic field polarities. We conclude that the observed DTs are very important parameters for the study of GCR transport in the heliosphere.