A successive approximation theory is developed for the hydrodynamics of journal bearing systems of finite length, the expansion parameter being the journal eccentricity. This is applied through the second approximation to full journal bearings of lengths exceeding the bearing perimeter. The existence of the lubricant source and associated end leakage is explicitly taken into account, it being assumed in the actual analysis that the source is set 90° in advance of the maximum film thickness. It is found that contrary to prevailing opinion, based on the infinitely long bearing theory, the friction coefficients and eccentricities for the systems are not uniquely determined by the ``Sommerfeld variable''—(r2/c2)(&mgr;N/P), wherer=journal radius,c=radial clearance, &mgr;=lubricant viscosity,N=journal speed in r.p.s.,P=bearing load per unit projected bearing area. It depends also on the leakage flux or source strength. For the position of source assumed in the analysis the friction coefficients and eccentricities increase with increasing source strengths. Further, the load carrying capacities of the finite length bearings are shown to be considerably less than for the infinitely long bearings, and decrease with increasing source strength if the source is placed in the low pressure part of the film. Finally, the theory shows how the consideration of the source of the lubricant permits a resolution of the difficulties with respect to the negative film pressures predicted by the infinitely long bearing theory. The numerical calculations show that the third and higher approximations may be neglected for eccentricity ratios not exceeding 0.4. General formulas are also developed for the asymptotic behavior of the friction coefficients on both the journal and bearing at very low eccentricities or large values of the Sommerfeld variable. These apply to bearings of all lengths and to partial as well as full journal bearings.