jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pThe cross-section of associated jats:italicJ/ψ</jats:italic>-jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) production in proton-proton collisions at a centre-of-mass energy of jats:inline-formulajats:alternativesjats:tex-math$$ \sqrt{s} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msqrt mml:mis</mml:mi> </mml:msqrt> </mml:math></jats:alternatives></jats:inline-formula> = 13 TeV is measured using a data sample corresponding to an integrated luminosity of 4jats:italic.</jats:italic>2 fbjats:supjats:italic−</jats:italic>1</jats:sup>, collected by the LHCb experiment. The measurement is performed for both jats:italicJ/ψ</jats:italic> and jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) mesons having transverse momentum jats:italicp</jats:italic>jats:subT</jats:sub>jats:italic<</jats:italic> 14 GeV/jats:italicc</jats:italic> and rapidity 2jats:italic.</jats:italic>0 jats:italic< y <</jats:italic> 4jats:italic.</jats:italic>5, assuming negligible polarisation of the jats:italicJ/ψ</jats:italic> and jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) mesons. The production cross-section is measured to be 4jats:italic.</jats:italic>5 ± 0jats:italic.</jats:italic>7 ± 0jats:italic.</jats:italic>3 nb, where the first uncertainty is statistical and the second systematic. The differential cross-sections are measured as functions of several kinematic variables of the jats:italicJ/ψ</jats:italic>-jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) candidates. The results are combined with a measurement of jats:italicJ/ψ</jats:italic>-jats:italicJ/ψ</jats:italic> production, giving a cross-section ratio between jats:italicJ/ψ</jats:italic>-jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) and jats:italicJ/ψ</jats:italic>-jats:italicJ/ψ</jats:italic> production of 0jats:italic.</jats:italic>274 ± 0jats:italic.</jats:italic>044 ± 0jats:italic.</jats:italic>008, where the first uncertainty is statistical and the second systematic.</jats:p>