When water flows in fractured reservoirs, it preferentially flows through the fractures. How rapidly the water penetrates into a fracture following;water injection depends on the crossflow rate into the adjacent matrix. This paper develops new analytical models that predict the location of the water front in the fracture in the presence of crossflow by capillary imbibition. In these models, the properties and dimensions of the medium on either side of the fracture can differ. These new models differ from existing models in that they do not assume that the local imbibition rate into the matrix is proportional to the local water saturation in the fracture. Evidence supporting this different view is presented. These new models predict that the water front in the fracture advances with the square root of time during the early-time period and linearly during the late-time period. Models for the oil flow rate and water-oil ratio along the fracture are also presented.