Polymer flooding in oil reservoir simulation is considered in two space dimensions. The wave structures associated with such a process give rise to interesting phenomena in the nonlinear regime which have direct bearing on the efficiency of oil recovery. These waves influence and can prevent surface instabilities of the fingering mode. In this paper we resolve these waves by a front tracking method. We consider the fingering problem and the issue of oil recovery for the polymer flood. The details of these two phenomena depend on the separation between the waves and upon the viscosity contrast between the oil, water and polymer. We identify a nonlinear transfer of instability between adjacent waves and a nonlinear enhancement of recovery due to successive waves. The conclusions produced by this work are also pertinent to tracer flooding.