The objective of the present invention is to provide an acrylic ester-based copolymer rubber which gives a rubber product excellent in fuel oil resistance and tensile strength and which is crosslinkable with sulfur and/or an organic peroxide and to provide a process for producing the same, as well as a rubber composition, an oil-resistant and weather-resistant rubber composition, and an oil-resistant and weather-resistant rubber product. The acrylic ester-based copolymer rubber of the present invention comprises a structural unit derived from at least one monomer selected from the group consisting of an acrylic acid alkyl ester and an acrylic acid alkoxyalkyl ester in an amount from 40 to 91.9% by mass, a structural unit derived from an unsaturated nitrile monomer in an amount from 8 to 40% by mass, and a structural unit derived from at least one monomer selected from the group consisting of a non-conjugated cyclic polyene and a compound having a specific structure in an amount from 0.1 to 20% by mass (provided 100% by mass of total of these), and has a Mooney viscosity [ML.sub.1+4(100.degree. C.)] in the range from 10 to 200.