\input zb-basic \input zb-ioport \iteman{io-port 06073870} \itemau{Jir\'askov\'a, Galina; Masopust, Tom\'a\v{s}} \itemti{Complexity in union-free regular languages.} \itemso{Int. J. Found. Comput. Sci. 22, No. 7, 1639-1653 (2011).} \itemab Summary: We continue the investigation of union-free regular languages that are described by regular expressions without the union operation. We also define deterministic union-free languages as languages accepted by one-cycle-free-path deterministic finite automata, and show that they are properly included in the class of union-free languages. We prove that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case. \itemrv{~} \itemcc{} \itemut{union-free regular language; finite automaton; one-cycle-free-path automaton; descriptional complexity; closure properties} \itemli{doi:10.1142/S0129054111008933} \end