Earlier earthquake cycle simulations using rate- and state-dependent friction (RSF) law have revealed that frictional coupling at a ruptured asperity starts immediately after dynamic slip because of logarithmically time-dependent healing. However, some Global Positioning System (GPS) inversion studies of the 2011 great Tohoku-Oki earthquake suggest that afterslip continued for 7–8 months or longer in the deep seismogenic interface including asperities where M7 earthquakes repeatedly occurred. Nakatani and Scholz  introduced the intrinsic cutoff time tcx in the logarithmically time dependent healing and pointed out that a long tcx could lead to delayed start of frictional coupling. Assuming RSF laws into which tcx was incorporated, we conducted a numerical simulation using a block spring model. We defined the time required to restore frictional coupling as Tcpl measured from the instant of dynamic slip. The value of Tcpl for tcx = 10−3 s was almost the same as Tcpl in the conventional law, which was on the order of 10 min in the case of the aging law. It increased approximately in proportion to tcx for short tcx (≤1 s), whereas Tcpl was not so sensitive to tcx for a long tcx (>1 s). Moreover, a long tcx cannot be reasonably assumed because the maximum slip velocity during dynamic slip decreased with increasing tcx, limiting the largest possible Tcpl to be months at most. Friction laws with two state variables, each having a different cutoff time, were also investigated. The maximum slip velocity was determined by the smaller cutoff time, and Tcpl was affected by the larger cutoff time. As a result, longer Tcpl became possible, although the values are still on time scale of months.