This paper focuses on task recognition and action segmentation in weakly-labeled instructional videos, where only the ordered sequence of video-level actions is available during training. We propose a two-stream framework, which exploits semantic and temporal hierarchies to recognize top-level tasks in instructional videos. Further, we present a novel top-down weakly-supervised action segmentation approach, where the predicted task is used to constrain the inference of fine-grained action sequences. Experimental results on the popular Breakfast and Cooking 2 datasets show that our two-stream hierarchical task modeling significantly outperforms existing methods in top-level task recognition for all datasets and metrics. Additionally, using our task recognition framework in the proposed top-down action segmentation approach consistently improves the state of the art, while also reducing segmentation inference time by 80-90 percent.