A sequential process combining laser beam micromachining(LBMM) and micro electro-discharge machining (μEDM) for the micro-drilling purpose was developed to incorporate both methods' benefits. In this sequential process, a guiding hole is produced through LBMM first, followed by μEDM applied to that same hole for more fine machining. This process facilitates a more stable, efficient machining regime with faster processing (compared to pure μEDM) and much better hole quality (compared to LBMMed holes). Studies suggest that strong correlations exist between the various input and output parameters of the sequential process. However, a mathematical model that maps and simultaneously predicts all these output parameters from the input parameters is yet to be developed. Our experimental study observed that the µEDM finishing operation's various output parameters are influenced by the morphological condition of the LBMMed holes. Hence, an artificial neural network(ANN) based dual-stage modelling method was developed to predict the sequential process's outputs. The first stage of the dual-stage model was utilized to predict various LBMM process outputs from different laser input parameters. Furthermore, in the second stage, LBMM predicted outputs (such as pilot hole entry area, exit area, recast layer, and heat affected zone) were used for the final prediction of the sequential process outputs (i.e. machining time by μEDM, machining stability during μEDM in terms of short circuit count and tool wear during μEDM). The model was evaluated based on the average RMSE (Root Mean Square Errors) values for the individual output parameters' complete set data, i.e. μEDM time, short circuit count and tool wear. The values of Average RMSE for the parameters as mentioned earlier were found to be 0.1272(87.28% accuracy), 0.1085(89.15% accuracy), 0.097 (90.3% accuracy), respectively.