During polymer flooding in oil reservoir, miscible and immiscible viscous fingering can occur at the front and backside of the polymer bank, respectively. Polymer dispersion and adsorption control the polymer concentration profile and water viscosity. So transport parameters should affect immiscible viscous instability between the oil and polymer banks. Earlier the effects of transport parameters on the miscible viscous instability and the effects of capillarity and relative permeability on immiscible viscous instability were studied. In this paper the effects of dispersivity and nonlinear adsorption on the growth of immiscible viscous fingers are discussed. We modeled equilibrium adsorption using a Langmuir isotherm. The pattern and growth of miscible and immiscible viscous fingers for different transport parameters were compared using the root mean square of unstable interfaces. We have found that like miscible viscous instability, the immiscible fingering is also less for higher longitudinal dispersivity. For larger transverse dispersivity, miscible viscous fingering is almost suppressed but immiscible fingers of large wavelength still grow. Adsorption does not affect miscible viscous instability behind the polymer bank, but it reduces the width of polymer bank. When the adsorption is very high, the miscible viscous fingers can puncture the polymer bank and reach the oil bank. In the case of strong nonlinear adsorption (large value of B in the Langmuir isotherm), the saturation profile is very sharp and immiscible viscous fingers grow fast. For linear adsorption or small B, the saturation front is diffused and immiscible viscous instability is greatly suppressed. So the linear adsorption model underpredicts the growth of the immiscible viscous finger. © 2019 by Begell House, Inc.