The naturally occurring nucleobase 5-methylcytosine (mC) and its oxidized derivatives 5-hydroxymethylcytosine (hmC), 5-formylcytosine (fC), and 5-carboxylcytosine (caC) play important roles in epigenetic regulation and, along with cytosine (C), represent nucleobases currently implicated in the active cytosine demethylation pathway. Despite considerable interest in these modified bases, their impact on the thermodynamic stability of double-stranded DNA (dsDNA) remains ambiguous and their influence on hybridization kinetics and dynamics is even less well-understood. To address these unknowns, we employ steady-state and time-resolved infrared spectroscopy to measure the influence of cytosine modification on the thermodynamics and kinetics of hybridization by assessing the impact on local base pairing dynamics, shifts in the stability of the duplex state, and changes to the hybridization transition state. Modification with mC leads to more tightly bound base pairing below the melting transition and stabilizes the duplex relative to canonical DNA, but the free energy barrier to dehybridization at physiological temperature is nevertheless reduced slightly. Both hmC and fC lead to an increase in local base pair fluctuations, a reduction in the cooperativity of duplex melting, and a lowering of the dissociation barrier, but these effects are most pronounced when the 5-position is formylated. The caC nucleobase demonstrates little impact on dsDNA under neutral conditions, but we find that this modification can dynamically switch between C-like and fC-like behavior depending on the protonation state of the 5-position carboxyl group. Our results provide a consistent thermodynamic and kinetic framework with which to describe the modulation of the physical properties of double-stranded DNA containing these modified nucleobases.