Tear strength is a very important mechanical property of polymer films and is associated with very fast deformation. In the present work, compressed and cast LLDPE films, made of resins with the same density, similar molecular weight but different comonomers (1-butene versus 1-octene), were studied with Elmendorf tear (very high deformation rate) and right angle tear (low deformation rate) methods, as well as small angle X-ray scattering (SAXS). Our study shows that the Elmendorf tear strength for the LLDPE with octene is much larger than that for the LLDPE with butene comonomer. However, no much difference in tear strength was observed for the two films with right angle testing method. The result indicates that the right angle method under low deformation rate, widely used in China for evaluation of tear strength for polymer films, may not reflect the true tear strength in actual applications. In order to have a better understanding of the fundamental differences for these two tear testing methods, structural studies were carried out for deformed films at low and very high strain rate (0.08 min(-1) versus 500 min(-1)). Our SAXS study shows that for a given deformation, such as for a strain of 0.5, much more structural damages were observed under fast deformation rate than that under low deformation rate, such as, leading to significantly smaller long period in the former case. That is, the structure response of polymer films to low and very fast deformation can be very different, and this could explain why a big difference is observed for tear testing with right angle and Elmendrof methods. Discussion were also made in the present paper on tear strength versus structures for LLDPE films made with different comonomers. Films can have very similar aggregated structure at different size levels, but with very different tear strength due to different tie change concentrations, which reflects the different crystal connectivity in the films and plays an important role on tear property.