Flow deformation and relaxation of mono- and bilayer domains of a thermotropic liquid crystal at the air-water interface have been studied by means of simultaneous application of extensional flow fields and Brewster angle microscopy measurements. In an extentional flow, mono- and bilayer domains are found to be distorted into long, stringlike domains that are stable. This is due to the absence of Rayleigh instabilities in the two-dimensional case, which otherwise lead to the occurrence of a break-up mechanism in three dimensions. However, small fluctuations in the domain thickness lead to defects that can cause breakup of the string domains followed by a retraction of the two domain ends due to line tension effects. In relaxation experiments covering both the high deformation bola-shaped regime and the small-deformation regime of slightly deformed domains, the line tensions of mono- and bilayer domains were determined. Both deformation regimes yielded the same values ibr the line tension of the mono- and bilayer cases. However, the line tension of the bilayer was found to be about 10 times higher than that of the monolayer. It is believed that this large difference is a result of a strong attractive dipole-dipole interaction force in the interdigitated bilayer.