Heart rate and Heart Rate Variability (HRV) are important measures that reflect the state of the cardiovascular system. HRV analysis has gained prominence in the field of cardiology for detecting cardiac abnormalities. This paper presents the study made on the use of linear (time domain and frequency domain) and nonlinear measures of heart rate variability for accurate classification of certain cardiac diseases. Three different classifiers, viz. Random Forests, Logistic Model Tree and Multilayer Perceptron Neural Network have been used for the classification. Data for use in this work has been obtained from the standard ECG databases in the Physionet website. Classification has been attempted using linear parameters, nonlinear parameters and combined. The classification results indicate that the combination of linear and nonlinear measures is a better indicator of heart diseases than linear or nonlinear measures alone. The results obtained by this study are comparable with those obtained with other techniques cited in the literature.