Real-time monitoring of downhole oil, gas and water flows in wells can significantly improve the production performance of these wells when this flow rate information is used to manipulate inflow control valves. An example of this is the allocation of a gas or water cone to its entrance point in a multilateral well, allowing to close down the individual well where the gas or water cone occurs, instead of closing down the complete well.Downhole monitoring of flows can be done via direct measurement. However, downhole multiphase metering is either expensive, inaccurate, or too difficult due to the harsh conditions. An alternative is to use softsensors. Softsensors estimate downhole holdups and flow rates from (relatively) cheap and reliable conventional downhole meters, such as pressure and temperature measurements, and a dynamic multiphase flow model connecting these measurements with the quantities of interest.Soft-sensing has already been investigated before for unilateral wells in Bloemen et al. (2004) and Leskens et al. (2008). In the second of these references, the simultaneous estimation of downhole oil, water and gas flows from downhole pressure and temperature measurements is considered. It is shown there that this estimation is badly conditioned (i.e. badly observable) and, thereby, not feasible in a practical situation. Using a similar approach and focussing on gas-lift wells, in Bloemen et al. (2004) it is suggested that soft-sensing with only downhole pressure and temperature measurements should work for the case that only a liquid and gas flow are estimated.In this paper, within the same soft-sensing framework as used in the mentioned two references, solutions are sought for soft-sensing of multilateral wells, both for the two-phase (gas and liquid) and three-phase (oil, water and gas) case.For that purpose, first, the question is addressed whether the unilateral two-phase case truly can be solved using only downhole pressure and temperature measurements. If so, the multilateral two-phase case is automatically solved with the corresponding soft-sensing solution simply consisting of a collection of unilateral two-phase sensors, one for each branch. It is shown that this solution is indeed feasible.After that, the three phase case is addressed. It is shown that for this case soft-sensing of multilateral wells is not possible, even when adding surface measurements and even though, as also shown here, it is possible for the unilateral well case when adding such measurements.