We study transcritical and pitchfork bifurcations in scalar nonautonomous difference equations. In the nonautonomous setting, these bifurcations are no longer described by isolated equilibria, but by bounded solutions and their stability properties.

Using explicitly solvable model equations as prototypes, we show that classical bifurcation scenarios persist via comparison with these model systems under suitable spectral and nonlinear balance conditions. Our approach is local in nature and applies when the dichotomy spectrum reduces to a single point, which allows it to depend smoothly on the parameter under additional summability assumptions.

Finally, we discuss the structural limitations of this approach, particularly when hyperbolicity is lost over a parameter interval, and indicate how it fits into the broader landscape of nonautonomous bifurcation theory.