For miscible pair of polyisoprene (PI) and poly(p-tert-butylstyrene) (PtBS), the component molecular weights, composition, and temperature were tuned to prepare PI/PtBS blends in the pseudomonodisperse state where the component PI and PtBS chains had the same terminal relaxation time, tau(1). These pseudomonodisperse blends had the linear viscoelastic moduli indistinguishable from the moduli of entangled monodisperse bulk homopolymers of particular molecular weights, and satisfied the time-strain separability in their nonlinear stress relaxation behavior under large step strains. The damping function h(gamma) of those blends was close to h(DE)(gamma) calculated from the Doi Edwards model and classified to be the so-called type-A damping function, even though the major component (PI) in the blends had a large entanglement number per chain (N >= 50). Highly entangled monodisperse homopolymers having similarly large N are known to exhibit the so-called type-C damping characterized by h(gamma) << h(DE)(gamma), and this damping behavior was indeed confirmed for high-M bulk PI utilized as the blend component. Thus, the nonlinear damping behavior was different for the pseudomonodisperse PI/PtBS blends and high-M bulk PI, despite the similarity in the entanglement number N for PI therein. This difference was discussed within the molecular scenario of Marrucci and Grizzuti in relation to the topological hindrance for PI segments due to PtBS segments having a much larger friction. This hindrance retarded the Rouse equilibration of the PI backbone in the blends, which possibly provided the highly entangled PI with a slow contour length fluctuation mechanism that competed with reptation. Such a competing mechanism smears the elastic instability underlying the type-C damping as suggested from the Marrucci Grizzuti scenario, which possibly allowed the pseudomonodisperse PI/PtBS blends containing highly entangled PI to exhibit the type-A damping. Furthermore, the type-A damping was observed also for a chemically homogeneous, highly entangled PI/PI blend being free from the topological hindrance for PI segments. In this PI/PI blends, the partial constraint release of the high-M component, activated by the relaxation of the low-M component, appeared to compete with reptation of the high-M component thereby smearing the instability and suppressing the type-C damping. Thus, the smearing of instability could be a rather universal feature occurring irrespective of the detail of the competing mechanisms.