We provide a process for making a base oil, comprising: a) selecting an olefin feed produced by thermal cracking of a waxy feed; b) oligomerizing the olefin feed in an ionic liquid oligomerization zone at a set of oligomerization conditions to form an oligomer; and c) alkylating the oligomer in the presence of an isoparaffin, in an ionic liquid alkylation zone, at a set of alkylation conditions to form an alkylated oligomeric product having a kinematic viscosity at 100.degree. C. of 6.9 mm.sup.2/s or greater, a VI of at least 134, and a Bromine Number of less than 4. We provide a process to make base oil from an olefin feed produced in a FCC unit. We also provide a process to make two or more viscosity grades of base oil from an olefin feed produced by thermal cracking of a waxy feed.