Relatively little work in the field of time series classification focuses on learning effectively from very large quantities of data. Large datasets present significant practical challenges in terms of computational cost and memory complexity.  We present strategies for extending two recent state-of-the-art methods for time series classification—namely, Hydra and Quant—to very large datasets. This allows for training these methods on large quantities of data with a fixed memory cost, while making effective use of appropriate computational resources. For Hydra, we fit a ridge regression classifier iteratively, using a single pass through the data, integrating the Hydra transform with the process of fitting the ridge regression model, allowing for a fixed memory cost, and allowing almost all computation to be performed on GPU. For Quant, we ‘spread’ subsets of extremely randomised trees over a given dataset such that each tree is trained using as much data as possible for a given amount of memory while minimising reads from the data, allowing for a simple tradeoff between error and computational cost. This allows for the straightforward application of both methods to very large quantities of data.  We demonstrate these approaches with results (including learning curves) on a selection of large datasets with between approximately 85, 000 and 47 million training examples.