The energy flow, dE/dη, is studied at large pseudorapidities in proton-proton collisions at the LHC, for centre-of-mass energies of 0.9 and 7 TeV. The measurements are made using the CMS detector in the pseudorapidity range 3.15 < |η| < 4.9, for both minimum-bias events and events with at least two high-momentum jets. The data are compared to various pp Monte Carlo event generators whose theoretical models and input parameter values are sensitive to the energy-flow measurements. Inclusion of multiple-parton interactions in the Monte Carlo event generators is found to improve the description of the energy-flow measurements.