The DØ Collaboration has studied for the first time the properties of hadron-collider jets reconstructed with a successive-combination algorithm based on relative transverse momenta (k⊥) of energy clusters. Using the standard value D=1.0 of the jet-separation parameter in the k⊥ algorithm, we find that the pT of such jets is higher than the ET of matched jets reconstructed with cones of radius R=0.7, by about 5 (8) GeV at pT≈90(240)GeV. To examine internal jet structure, the k⊥ algorithm is applied within D=0.5 jets to resolve any subjets. The multiplicity of subjets in jet samples at √s=1800GeV and 630 GeV is extracted separately for gluons (Mg) and quarks (Mq), and the ratio of average subjet multiplicities in gluon and quark jets is measured as (⟨Mg⟩−1)/(⟨Mq⟩−1)=1.84±0.15(stat)±0.220.18(syst). This ratio is in agreement with the expectations from the HERWIG Monte Carlo event generator and a resummation calculation, and with observations in e+e− annihilations, and is close to the naive prediction for the ratio of color charges of CA/CF=9/4=2.25. Received 4 September 2001DOI:https://doi.org/10.1103/PhysRevD.65.052008©2002 American Physical Society