This paper presents the results of two spectral-line very long baseline (VLB) interferometric experiments on stellar OH masers. These masers are usually associated with long-period variable stars, and exhibit a characteristic double-peaked 1612 MHz OH spectrum. The sources IRC +10011, R Aql, and U Ori were carefully studied in order to determine the spatial structure of their masers. Maser components in these sources exhibited a complex structure which can be interpreted in terms of ''core-halo'' models. For these sources, the emission at any velocity appears to originate from a small (approximately-less-than0.''03) region of brightness approximately-greater-than10/sup 9/ K, and from a large (approximately-greater-than0.''5) region of brightness approximately-less-than10/sup 8/ K. In IRC+10011, ''core'' components in the two OH peaks probably are separated by less than the apparent size of the ''halos.'' A map of the low-velocity emission of U Ori with a resolution of 0.''01 indicates that the ''cores'' are distributed over a region of only 0.''2. This region is smaller than the apparent sizes of the ''halos.'' Other sources surveyed to determine apparent maser sizes include IRC+50137, OH 1821--12, OH 1837--05, OH 26.5+0.6, W43 A, and VX Sgr at 1612 MHz; and W Hya, R Aql, and IRC--10529 at 1667 MHz.more » The results of all VLB observations of 1612 MHz stellar OH masers are summarized.The apparent sizes of the strongest components (''halos'') of stellar OH masers typically are approximately-greater-than0.''5, corresponding to linear dimensions of approximately-greater-than3 x 10/sup 15/ cm. These surprisingly large sizes imply brightness temperatures much lower than those observed in most other types of astronomical masers. The large sizes rule out models of the 1612 MHz OH masers that require contracting or rotating circumstellar envelopes to explain the double-peaked OH spectra, or that try to explain the apparent maser sizes by interstellar or interplanetary scattering.« less