We report the discovery of a new planetary system around the K giant \eta Cet ( HIP 5364 , HD 6805 , HR 334 ) based on 118 high-precision optical radial velocities taken at Lick Observatory since July 2000 . Since October 2011 an additional nine near-infrared Doppler measurements have been taken using the ESO CRIRES spectrograph ( VLT , UT1 ) . The visible data set shows two clear periodicities . Although we can not completely rule out that the shorter period is due to rotational modulation of stellar features , the infrared data show the same variations as in the optical , which strongly supports that the variations are caused by two planets . Assuming the mass of \eta Cet to be 1.7 ~ { } M _ { \odot } , the best edge-on coplanar dynamical fit to the data is consistent with two massive planets ( m _ { b } ~ { } \sin i~ { } = ~ { } 2.6 ~ { } \pm~ { } 0.2 ~ { } M _ { \mathrm { Jup } } , m _ { c } ~ { } \sin i~ { } = ~ { } 3.3 ~ { } \pm~ { } 0.2 ~ { } M _ { \mathrm { Jup } } ) , with periods of P _ { b } = 407 \pm 3 days and P _ { c } = 740 \pm 5 days and eccentricities of e _ { b } = 0.12 \pm 0.05 and e _ { c } = 0.08 \pm 0.03 . These mass and period ratios suggest possible strong interactions between the planets , and a dynamical test is mandatory . We tested a wide variety of edge-on coplanar and inclined planetary configurations for stability , which agree with the derived radial velocities . We find that for a coplanar configuration there are several isolated stable solutions and two well-defined stability regions . In certain orbital configurations with moderate e _ { b } eccentricity , the planets can be effectively trapped in an anti-aligned 2:1 mean motion resonance that stabilizes the system . A much larger non-resonant stable region exists in low-eccentricity parameter space , although it appears to be much farther from the best fit than the 2:1 resonant region . In all other cases , the system is categorized as unstable or chaotic . Another conclusion from the coplanar inclined dynamical test is that the planets can be at most a factor of \sim 1.4 more massive than their suggested minimum masses . Assuming yet higher inclinations , and thus larger planetary masses , leads to instability in all cases . This stability constraint on the inclination excludes the possibility of two brown dwarfs , and strongly favors a planetary system .