jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pRelations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, with a focus on duality invariant (2jats:italicn −</jats:italic> 1)-form electrodynamics and chiral 2jats:italicn</jats:italic>-form electrodynamics in Minkowski spacetime of dimension jats:italicD</jats:italic> = 4jats:italicn</jats:italic> and jats:italicD</jats:italic> = 4jats:italicn</jats:italic> + 2, respectively. We exhibit a new family of chiral 2-form electrodynamics in jats:italicD</jats:italic> = 6 for which these limits exhaust the possibilities for conformal invariance; the weak-field limit is related by dimensional reduction to the recently discovered ModMax generalisation of Maxwell’s equations. For jats:italicn ></jats:italic> 1 we show that the chiral ‘strong-field’ 2jats:italicn</jats:italic>-form electrodynamics is related by dimensional reduction to a new jats:italicSl</jats:italic>(2; ℝ)-duality invariant theory of (2jats:italicn −</jats:italic> 1)-form electrodynamics.</jats:p>