[en] We present a study of J/ψ meson production in collisions of 26.7 GeV electrons with 820 GeV protons, performed with the H1-detector at the HERA collider at DESY. The J/ψ mesons are detected via their leptonic decays both to electrons and muons. Requiring exactly two particles in the detector, a cross section of σ(ep→J/ψX)=(8.8±2.0±2.2) nb is determined for 30 GeV≤W_γp≤180 GeV and Q²< or ∼4 GeV². Using the flux of quasi-real photons with Q²< or ∼4 GeV², a total photoproduction cross section of σ(γp→J/ψX)=(56±13±14) nb is derived at an average W_γp=90 GeV. The distribution of the squared momentum transfer t from the proton to the J/ψ can be fitted using an exponential exp(-bvertical stroke tvertical stroke ) below avertical stroke tvertical stroke of 0.75 GeV² yielding a slope parameter of b=(4.7±1.9) GeV^-2. (orig.)