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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 = 1800 GeV 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) ±-0.18+0.22 (syst). This ratio is in agreement with the expectations from the HERWIG Monte Carlo event generator and a resummation calculation, and with observations in e1e2 annihilations, and is close to the naive prediction for the ratio of color charges of CA /CF=9/4 =2.25.