The Purpose of this study is to develop the rainfall-delayed response model (RDR Model) which influences the baseflow proportion of rivers as a result of the antecedent precipitation of the previous several months. The assesment of accurate baseflows in the rivers is one of the most important elements for the planning of seasonal water supply for agriculture, water resources development, hydrological studies for the availability of water and design criteria for various irrigation facilities. The Palukan river gauging site which is located in the Pulukan catchment on Bali Island, Indonesia was selected to develop this model. The basic data which has been used comprises the available historic flow records at 19 hydrologic gauging stations and 77 rainfall stations on Bali Island in the study. The methology adopted for the derivation of the RDR model was the water balance equation which is commonly used for any natural catcbment ie.P=R+(catchment losses) -R+(ET+DP+DSM+DGW). The catchment losses consist of evapotranspiration, deep percolation. change in soil moisture, and change in groundwater storage. The catchment areal rainfall has been generated by applying the combination method of Thiessen polygon and Isohyetal lines in the studies. The results obtained from the studies may be summarized as follows ; 1. The rainfall-runoff relationship derived from the water balance equation is as shown below, assuming a relationship of the form Y=AX+B. Finally these two equations for the annual runoff were derived ; ARO$_1$=0.855 ARF-821, ARF>=l,400mm ARO$_2$=0.290ARF- 33, ARF<1,400mm 2. It was found that the correction of observed precipitation by a combination of Thiessen polygons and Isohyetal lines gave good correlation. 3. Analysis of historic flow data and rainfall, shows that surface runoff and base flow are 52 % and 48% (equivalent to 59.4 mm) of the annual runoff, respectively. 4. Among the eight trial RDR models run, Model C provided the correlation with historic flow data. The number of months over which baseflow is distributed and the relative proportions of rainfall contributing in each month, were estimated by performing several trial runs using data for the Pulukan catchment These resulted in a value for N of 4 months with contributing proportions of 0.45, 0.50, 0.03 and 0.02. Thus the baseflow in any month is given by : P$_1$(n) =0.45 P(n) +0.50 P(n-I ) +0.03 P(n-$_2$) +0.02 P(n-$_3$) 5. The RDR model test gave estimated flows within +3.4 % and -1.0 % of the observed flows. 6. In the case of 3 consecutive no rain months, it was verified that 2.8 % of the dependable annual flow will be carried over the following year and 5.8 % of the potential annual baseflow will be transfered to the next year as a result of the rainfall-delayed response. The results of evaluating the pefformance of the RDR Model was generally satisfactory.