The disturbance decoupling and the simultaneous disturbance and input-output decoupling problems for singular systems are considered in the context of the matrix fraction description (MFD) of the system. Solvability conditions are obtained in terms of the composite matrix of a column reduced MFD of the system, a characterisation of the fixed poles of both problems is given and it is shown that the remaining poles can be arbitrarily assigned. (C) 2012 Elsevier Ltd. All rights reserved.