NOVELTY - Producing (M1) a lube base stock and/or a diesel fuel from a feedstock of biological origin, involves: contacting the feedstock in a single reactor in the presence of hydrogen with catalyst components comprising a first catalyst and a second catalyst, where the first catalyst comprises an acidic material and/or a basic material, where the second catalyst comprises a hydrogenation catalyst and a hydrothermally stable binder.    USE - For producing a lube base stock or a diesel fuel from a feedstock of biological origin in a single reactor (claimed).    ADVANTAGE - The acid catalysts allow for conversion of triglycerides to fatty acid dimers and oligomers without requiring addition of water for an initial hydrolysis reaction, although water can be optionally added to the reactor. The presence of hydrogen reduces the cyclic oligomer formation. This is beneficial for production of high paraffinic hydrocarbons at the end of the conversion.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) making (M2) a lube base stock and/or a diesel fuel from a feedstock of biological origin in a single reactor, involving: a) converting a feedstock of biological origin comprising a triglyceride to a fatty acid; b) coupling the fatty acid to a ketone and/or a heavier oxygenate with a basic catalyst, and/or dimerizing the fatty acid to a dimer acid and a higher oligomer with an acidic catalyst; and c) hydrogenating the ketone, the heavier oxygenate, the dimer acid and/or the oligomer to a hydrocarbon with a catalyst comprising a hydrogenation catalyst and a hydrothermally stable binder; and    (2) a lube base stock prepared from a biologically derived oil comprising a fatty acid, a fatty acid ester, a fatty alcohol, a fatty olefin, a mono-glyceride, a di-glyceride or a tri-glyceride, comprising not greater than 20 wt.% 2-ring naphthenic, at least 20 wt.% paraffin, and not greater than 60 wt.% 1-ring naphthenic, as determined by two-dimensional gas chromatography.