Neural Networks have been found useful in many biomedical applications. The purpose of this paper is to apply Neural Networks (NN) to two specific problems in cardiology, namely, diagnosis of echocardiograms for myocardial infarction and prediction of vital status of patients that suffered such. We used NN to discriminate between normal and infarcted myocardium, by looking at intensity changes. The intensities of selected regions are used for training and testing. In predicting the vital status of patients that have suffered acute myocardial infarction, we used a large database (MIDAS) with follow-ups. The NN in this case has two hidden layers with eighteen patient variables from the MIDAS dataset as inputs. The NN was again trained with the feedback algorithm ALOPEX and tested with unknown data.