Thyroid nodule segmentation and classification in ultrasound images are two essential but challenging tasks for computer-aided diagnosis of thyroid nodules. Since these two tasks are inherently related to each other and sharing some common features, solving them jointly with multi-task leaning is a promising direction. However, both previous studies and our experimental results confirm the problem of inconsistent predictions among these related tasks. In this paper, we summarize two types of task inconsistency according to the relationship among different tasks: intra-task inconsistency between homogeneous tasks (e.g., both tasks are pixel-wise segmentation tasks); and inter-task inconsistency between heterogeneous tasks (e.g., pixel-wise segmentation task and categorical classification task). To address the task inconsistency problems, we propose intra- and inter-task consistent learning on top of the designed multi-stage and multi-task learning network to enforce the network learn consistent predictions for all the tasks during network training. Our experimental results based on a large clinical thyroid ultrasound image dataset indicate that the proposed intra- and inter-task consistent learning can effectively eliminate both types of task inconsistency and thus improve the performance of all tasks for thyroid nodule segmentation and classification.Copyright © 2022 Elsevier B.V. All rights reserved.