High Efficiency Video Coding (HEVC) is the latest international video coding standard. As an extension of HEVC, scalable HEVC (SHVC) achieves high compression efficiency at the cost of dramatically increased computational complexity. In this paper, a fast Coding Unit (CU) size decision algorithm is suggested for spatial SHVC intra-coding to early terminate the CU size decision process by jointly utilising the inter-layer and spatiotemporal correlations. Furthermore, in order to realise a fast Prediction Unit (PU) intra-mode decision, the mode dependency between the Base Layer (BL) and the Enhancement Layer (EL) is effectively used to remove unlikely coding modes. A fast PU inter-mode decision method is also developed for spatial SHVC inter-coding, in which the degree of motion activity and the PU mode dependency are exploited. Simulation results show that the proposed fast intra-coding algorithm produces a saving in encoding time of up to 72% and the proposed fast inter-coding scheme reduces the encoding time by up to 50% compared with the original SHVC encoder, and the loss in Rate-Distortion (RD) performance is negligible.