The ALICE Collaboration reports three measurements in ultraperipheral proton-lead collisions at forward rapidity. The exclusive two-photon process γγ→μ+μ- and the exclusive photoproduction of J/ψ are studied. J/ψ photoproduction with proton dissociation is measured for the first time at a hadron collider. The cross section for the two-photon process of dimuons in the invariant mass range from 1 to 2.5 GeV/c2 agrees with leading-order quantum electrodynamics calculations. The exclusive and dissociative cross sections for J/ψ photoproductions are measured for photon-proton center-of-mass energies from 27 to 57 GeV. They are in good agreement with HERA results.