Neutron and proton driplines of single-Λ and double-Λ hypernuclei, Ξ- hypernuclei as well as normal nuclei are studied within a relativistic mean field approach using an extended form of the FSU Gold Lagrangian density. Hyperons are found to produce bound nuclei beyond the normal nuclear driplines. Radii are found to decrease in hypernuclei near the driplines, in line with observations in light Λ hypernuclei near the stability valley. The inclusion of a Ξ- introduces a much larger change in radii than one or more Λ's. © 2013 World Scientific Publishing Company.