jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pThe associated production of prompt jats:italicJ/ψ</jats:italic> and jats:italicΥ</jats:italic> mesons in jats:italicpp</jats:italic> 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 studied using LHCb data, corresponding to an integrated luminosity of 4 fbjats:supjats:italic−</jats:italic>1</jats:sup>. The measurement is performed for jats:italicJ/ψ</jats:italic> (jats:italicΥ</jats:italic>) mesons with a transverse momentum jats:italicp</jats:italic>jats:subT</jats:sub>jats:italic<</jats:italic> 10 (30) GeV/jats:italicc</jats:italic> in the rapidity range 2jats:italic.</jats:italic>0 jats:italic< y <</jats:italic> 4jats:italic.</jats:italic>5. In this kinematic range, the cross-section of the associated production of prompt jats:italicJ/ψ</jats:italic> and jats:italicΥ</jats:italic>(1jats:italicS</jats:italic>) mesons is measured to be 133 ± 22 ± 7 ± 3 pb, with a significance of 7jats:italic.</jats:italic>9 jats:italicσ</jats:italic>, and that of prompt jats:italicJ/ψ</jats:italic> and jats:italicΥ</jats:italic>(2jats:italicS</jats:italic>) mesons to be 76 ± 21 ± 4 ± 7 pb, with a significance of 4jats:italic.</jats:italic>9 jats:italicσ</jats:italic>. The first uncertainty is statistical, the second systematic, and the third due to uncertainties on the used branching fractions. This is the first observation of the associated production of jats:italicJ/ψ</jats:italic> and jats:italicΥ</jats:italic>(1jats:italicS</jats:italic>) in proton-proton collisions. Differential cross-sections are measured as functions of variables that are sensitive to kinematic correlations between the jats:italicJ/ψ</jats:italic> and jats:italicΥ</jats:italic>(1jats:italicS</jats:italic>) mesons. The effective cross-sections of the associated production of prompt jats:italicJ/ψ</jats:italic> and jats:italicΥ</jats:italic> mesons are obtained and found to be compatible with measurements using other particle productions.</jats:p>