Spontaneous imbibition experiments are usually carried out on All Faces Open or One End Open cores and this severely limits the information that can be obtained because imbibition can be approximately described with a square root of time function, which involves only a single variable. Two Ends Open with one end in contact with the brine and the other end in contact with oil (at the same pressure) offers much more varied behaviour because imbibition is partly co-current and partly counter-current. Previously, an analysis and experiments were described for primarily co-current imbibition when the viscosities of the oil and brine were close to equal. Small deviations from the square root of time relationship allowed parameters such as the capillary back pressure (bubble pressure) to be determined. In the present paper, the situation when the oil is significantly more viscous than the brine is analysed and compared with experiments. The results show that counter-current imbibition continues for almost the entire imbibition period. They also show that the relative permeability to oil behind the front varies as the viscosity ratio is changed. Very viscous oil gives higher relative permeability than less viscous oil.