Purpose Slender boring bars vibrate when excited by cutting forces to result in chatter. These chatter vibrations damage the part and the tool and hence must be avoided and/or suppressed. Usually, tuned absorbers integrated within the boring bar dissipate the motion of the boring bar and make stable cutting possible. However, since the boring bar's dynamics change with loading and boundary conditions, optimally tuning the absorber becomes difficult. This prevents stable highperformance cutting. To improve the cutting performance of a potentially detuned absorber within a boring bar, this paper presents a novel hybrid damping solution. The hybrid damper is composed of an absorber working in conjunction with an eddy current damper. Methods To demonstrate the working of this hybrid damper, we model the boring bar as an Euler-Bernoulli beam. A permanent magnet is supported by a spring and damper within a copper section of a boring bar. The supported magnet acts as an absorber and the relative motion between the conductive copper bar and the magnetic field induces eddy currents that hinder the motion of the boring bar. Governing equations for the beam with an integrated damper are obtained by applying the extended Hamilton's principle. Eddy current damping is evaluated by applying the Lorentz force law and the Biot-Savart law. Results Our analysis suggests that the improvement in the chatter-free depth of cut with a hybrid damper over the case with a detuned absorber is as much as similar to 500%. And, when the absorber is optimally tuned and the hybrid damper takes its maximum possible value, the chatter-free depth of cut for both cases was found to be the same, suggesting that if/when the absorber can be optimally tuned, the eddy current damper offers no additional benefit. Conclusion Since optimally tuning an absorber is difficult, our proposed hybrid damper offers a feasible solution to improve cutting performance with slender boring bars. Moreover, since our models are generalized, the approach may also be used to explore the integration of such hybrid dampers within other tooling systems such as milling tool holders.