Abstract: We explore cosmological constraints on the sum of the three active neutrino masses M-v in the context of dynamical dark energy (DDE) models with equation of state (EoS) parametrized as a function of redshift z by w(z) = w(0) + w(a)z/ (1 + z), and satisfying w(z) >= -1 for all z. We make use of cosmic microwave background data from the Planck satellite, baryon acoustic oscillation measurements, and supernovae la luminosity distance measurements, and perform a Bayesian analysis. We show that, within these models, the bounds on M-v do not degrade with respect to those obtained in the Lambda CDM case; in fact, the bounds arc slightly tighter, despite the enlarged parameter space. We explain our results based on the observation that, for fixed choices of w(0), w(a) such that w(z) >= -1 (but not w = -1 for all z), the upper limit on M-v is tighter than the Lambda CDM limit because of the well-known degeneracy between w and M-v. The Bayesian analysis we have carried out then integrates over the possible values of w(0)-w(a) such that w(z) >= -1, all of which correspond to tighter limits on M-v than the Lambda CDM limit. We find a 95% credible interval (C.I.) upper bound of M-v < 0.13 eV. This bound can be compared with the 95% C.I. upper bounds of M-v < 0.16 eV, obtained within the Lambda CDM model, and M-v < 0.41 eV, obtained in a DDE model with arbitrary EoS (which allows values of w < -1). Contrary to the results derived for DDE models with arbitrary EoS, we find that a dark energy component with w(z) >= -1 is unable to alleviate the tension between high-redshift observables and direct measurements of the Hubble constant H o . Finally, in light of the results of this analysis, we also discuss the implications for DDE models of a possible determination of the neutrino mass ordering by laboratory searches.