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We study the dynamical models of two massive nearby early-type galaxies, NGC 4473 and NGC 4697, using globular clusters (GCs) as tracers of their gravitational potential. We use their velocity dispersion to model their dynamics based on solving the spherical Jeans equation in both Newtonian and MOdified Newtonian Dynamics (MOND) approaches. We take into account the orbital anisotropies and we model the following three cases: we study isotropic, tangentially and radially anisotropic models interior to ∼12 effective radii for NGC 4473 and interior to ∼3 effective radii for NGC 4697. We analyse these two galaxies that are part of the larger SLUGGS sample because we obtained photometric data using the new 1.40 m telescope 'Milanković' for both objects to estimate the contribution of the visible, stellar, component, using several stellar population synthesis models as priors. In addition to three widely analysed MOND models (standard, simple, and toy) for the first time in the literature we analyse the Zhao MOND model on elliptical galaxies. We also analysed several additional MOND models found in the literature and we also tested the Einasto dark matter models. We find that in the Newtonian approach, both galaxies in general may need dark matter to describe their kinematics. The best-fitting results were in both cases obtained with the inclusion of the dark matter halo but we managed to find solutions for which the dark component is not needed. We also find that both galaxies may be well modelled using all the tested MOND functions assuming the existence of the visible matter only. © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.