AbstractResults on $ϕ $ϕ meson production in inelastic $p + p$p+p collisions at CERN SPS energies are presented. They are derived from data collected by the NA61/SHINE fixed target experiment, by means of invariant mass spectra fits in the $ϕ → K^+ K^- $ϕ→K+K- decay channel. They include the first ever measured double differential spectra of $ϕ $ϕ mesons as a function of rapidity $y$y and transverse momentum $p_{\text {T}}$pT for proton beam momenta of $80 \, \hbox {GeV}/c$80GeV/c and $158 \, \hbox {GeV}/c$158GeV/c, as well as single differential spectra of $y$y or $p_{\text {T}}$pT for beam momentum of $40 \, \hbox {GeV}/c$40GeV/c. The corresponding total $ϕ $ϕ yields per inelastic $p + p$p+p event are obtained. These results are compared with existing data on $ϕ $ϕ meson production in $p + p$p+p collisions. The comparison shows consistency but superior accuracy of the present measurements. The emission of $ϕ $ϕ mesons in $p + p$p+p reactions is confronted with that occurring in $\mathrm{Pb} + \mathrm{Pb}$Pb+Pb collisions, and the experimental results are compared with model predictions. It appears that none of the considered models can properly describe all the experimental observations.