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Compound character recognition of Devanagari script is one of the challenging tasks since the characters are complex in structure and can be modified by writing combination of two or more characters. These compound characters occurs 12 to 15% in the Devanagari Script. The moment based techniques are being successfully applied to several image processing problems and represents a fundamental tool to generate feature descriptors where the Zernike moment technique has a rotation invariance property which found to be desirable for handwritten character recognition. This paper discusses extraction of features from handwritten compound characters using Zernike moment feature descriptor and proposes SVM and k-NN based classification system. The proposed classification system preprocess and normalize the 27000 handwritten character images into 30x30 pixels images and divides them into zones. The pre-classification produces three classes depending on presence or absence of vertical bar. Further Zernike moment feature extraction is performed on each zone. The overall recognition rate of proposed system using SVM and k-NN classifier is upto 98.37%, and 95.82% respectively.