Hulu is capable of lowering the video quality of a stream based on the quality of the viewer's internet speed, so it is possible to watch shows on Hulu without great internet. However, Hulu does recommend some minimum download speeds if you want to experience the best possible picture quality:

On-demand shows and movies: 1.5+ Mbps for standard definition video, and 3+ Mbps for high definition video.
Live television: 8+ Mbps for a single stream, and additional bandwidth to view multiple streams.

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