A Leslie-Gower type predator-prey model including group defense for-mation is analyzed. This phenomenon, described by a non-monotonic function origi-nates interesting dynamics; positiveness, boundedness, permanence of solutions, andexistence of up to three positive equilibria are established. The solutions are highlysensitive to initial conditions since there exists a separatrix curve dividing their be-havior. Two near trajectories can have far omega-limit sets. The weakness of asingularity is established showing two limit cycles can exist. Numerical simulationsendorse the analytical outcomes