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We introduce new analogues of the Ramanujan sums, denoted by$\widetilde{c}_q(n)$, associated with unitary divisors, and obtain resultsconcerning the expansions of arithmetic functions of several variables withrespect to the sums $\widetilde{c}_q(n)$. We apply these results to certainfunctions associated with $\sigma^*(n)$ and $\phi^*(n)$, representing theunitary sigma function and unitary phi function, respectively.

Expansions of arithmetic functions of several variables with respect to certain modified unitary Ramanujan sums