Present work involves rigorous experimentation for classification of mammographic masses by employing four deep transfer learning models using hierarchical framework. Experimental work is carried on 518 SFM images of DDSM dataset with 208, 150 and 160 images of probably benign, suspicious- malignant and highly malignant classes, respectively. ResNet50 model is used for generating segmented mass images. For hierarchical classification framework, at node 1, the segmented mass image is classified as belonging to probably benign (BIRAD-3) class or suspicious abnormality (BIRAD-4 and BIRAD-5) class. At node 2, the segmented mass image belonging to suspicious abnormality class is further classified as suspicious malignant (BIRAD-4) class or highly malignant (BIRAD-5) class. Deep transfer learning based hierarchical CAD systems experimented in the present work include VGG16/VGG19/ GoogleNet/ResNet50 models. It was noted that deep transfer learning model VGG19 at node 1 and VGG16 at node 2, yielded highest classification accuracy of 93 % and 90 %, respectively, therefore, a deep transfer learning based hybrid hierarchical CAD system was developed by employing VGG19 at node 1 and VGG16 at node 2. This model yields overall classification accuracy of 88 %. Further, hybrid hierarchical CAD system was designed using VGG19/ANFC-LH classifier at node 1, and VGG16/ANFC-LH classifier at node 2 yielding the highest classification accuracy of 92%. The promising result yielded by hybrid hierarchical CAD system design indicates its usefulness for step-wise classification of mammographic masses.