We report the results of a spectroscopic and polarimetric study of the massive , hydrogen-rich WN6h stars R144 ( HD 38282 = BAT99-118 = Brey 89 ) and R145 ( HDE 269928 = BAT99-119 = Brey 90 ) in the LMC . Both stars have been suspected to be binaries by previous studies ( R144 : Schnurr et al . 30 ; R145 : Moffat 18 ) . We have combined radial-velocity ( RV ) data from these two studies with previously unpublished polarimetric data . For R145 , we were able to establish , for the first time , an orbital period of 158.8 days , along with the full set of orbital parameters , including the inclination angle i , which was found to be i = 38 ^ { \circ } \pm 9 ^ { \circ } . By applying a modified version of the shift-and-add method developed by Demers et al . ( 7 ) , we were able to isolate the spectral signature of the very faint-line companion star . With the RV amplitudes of both components in R145 , we were thus able to estimate their absolute masses . We find minimum masses M _ { WR } sin ^ { 3 } i = ( 116 \pm 33 ) M _ { \odot } and M _ { O } sin ^ { 3 } i = ( 48 \pm 20 ) M _ { \odot } for the WR and the O component , respectively . Thus , if the low inclination angle were correct , resulting absolute masses of the components would be at least 300 and 125 M _ { \odot } , respectively . However , such high masses are not supported by brightness considerations when R145 is compared to systems with known , very high masses such as NGC3603-A1 or WR20a . An inclination angle close to 90 ^ { \circ } would remedy the situation , but is excluded by the currently available data . More and better data are thus required to firmly establish the nature of this puzzling , yet potentially very massive and important system . As to R144 , however , the combined data sets are not sufficient to find any periodicity .