The paper studies monetary and fiscal policy rules consistent with determinate equilibrium dynamics. We consider a three-dimensional New Keynesian model in continuous time with Rotemberg price-setting mechanism and non-Ricardian consumers, and study dynamics of the model under monetary and fiscal policies interactions. The key analytical finding is that the uniqueness of the equilibrium solution can be never achieved while both policies are in their active regimes. Another combinations of policies' regimes can lead to a local equilibrium determinacy through control of appropriate values of Taylor coeffcients (f^Mand f^F). We demonstrate that in contrast to economy with Ricardian consumers, making government debt a net asset leads to creation of an additional channel for fiscal and monetary policy interaction and changing the conditions for local equilibrium determinacy. In addition, we show that in case of explosive equilibrium dynamics, limit cycle or more complicated attracting sets could appear, including chaotic attractors of various natures.