Various types of singularly perturbed boundary-value prohiems arising in discrete systems are Iormulatcd. For the general type it is seen that the degenerate problem is of reduced-order and hence shows its inability to accommodate all the given bounderv conditions. These left-over boundary condit.ions arc readmitted through e.ppropr-iat c corrections for the initial and final boundary layers. A perturhation methOI’ i:-l developed to obt.ain an approximate solution composed of an outer series, initial boundary layer correction series and final boundary layer correct.ion series. An important feature of t.he method is that the eorrnct.ions for the original boundary-vuluu problem are solved as an initial-value problem and a final-value problem, facilitating a considerable reduction in computation. An example i:-; given to dcmonst rat o tilt’ method.