Recommending the right products is the central problem in recommender systems, but the right products should also be recommended at the right time to meet the demands of users, so as to maximize their values. Users' demands, implying strong purchase intents, can be the most useful way to promote products sales if well utilized. Previous recommendation models mainly focused on user's general interests to find the right products. However, the aspect of meeting users' demands at the right time has been much less explored. To address this problem, we propose a novel Long-Short Demands-aware Model (LSDM), in which both user's interests towards items and user's demands over time are incorporated. We summarize two aspects: termed as long-time demands (e.g., purchasing the same product repetitively showing a long-time persistent interest) and short-time demands (e.g., co-purchase like buying paintbrushes after pigments). To utilize such long-short demands of users, we create different clusters to group the successive product purchases together according to different time spans, and use recurrent neural networks to model each sequence of clusters at a time scale. The long-short purchase demands with multi-time scales are finally aggregated by joint learning strategies. Experimental results on three real-world commerce datasets demonstrate the effectiveness of our model for next-item recommendation, showing the usefulness of modeling users' long-short purchase demands of items with multi-time scales.