  We report on the realization of quantum degenerate gas mixtures of the
alkaline-earth element strontium with the alkali element rubidium. A key
ingredient of our scheme is sympathetic cooling of Rb by Sr atoms that are
continuously laser cooled on a narrow linewidth transition. This versatile
technique allows us to produce ultracold gas mixtures with a phase-space
density of up to 0.06 for both elements. By further evaporative cooling we
create double Bose-Einstein condensates of 87Rb with either 88Sr or 84Sr,
reaching more than 10^5 condensed atoms per element for the 84Sr-87Rb mixture.
These quantum gas mixtures constitute an important step towards the production
of a quantum gas of polar, open-shell RbSr molecules.
