An ensemble of single domain magnetic nanoparticles often tends to form chains and clusters of various geometries to reduce the micromagnetic energies. The magnetic behavior is different when the nanoparticles are exchange coupled rather than physically separated and only dipolar coupled. Here, we have studied the quasistatic magnetization reversal mechanisms of chains and clusters of exchange-coupled magnetic nanoparticles by experimental and micromagnetic simulation methods. We have explained the experimental magnetic hysteresis behaviors by using the finite element method (FEM) based micromagnetic simulations. We observe that the magnetization reversals in these samples occur through the formation of various local domain states including vortices and fanning- and curling-like modes, depending upon the cluster geometry. The constituent nanoparticles reverse by the quasi-coherent rotation of magnetization, whereas the incoherence between the nanoparticles in the cluster gives rise to the observed domain structures.