  We extended to the R and I bands the light curve coverage for 8 Cepheids
already studied in B and V by Capaccioli et al [AJ, 103, 1151 (1992)]. Sixteen
additional Cepheid candidates have been identified and preliminary periods are
proposed. The new Cepheids allow the period-luminosity relation to be extended
one magnitude fainter. Apparent B, V, R, and I distance moduli have been
calculated. Combining the data at different wavelengths, and assuming a true
distance modulus of 18.50 mag for the LMC, we obtain for NGC 3109 a true
distance modulus $(m-M)_0=25.67\pm0.16$, corresponding to $1.36\pm0.10$ Mpc.
Adopting $E(B-V)=0.08$ for the LMC, the interstellar reddening for the Cepheids
in NGC 3109 is consistent with 0. A discussion on the possible implications of
this result is presented. A comparison of the period-color, period-amplitude,
and period-luminosity relations suggests similar properties for the Cepheids in
the LMC, NGC 3109, Sextans A, Sextans B, and IC 1613, though the uncertainties
in the main parameter determination are still unsatisfactorily high for a firm
conclusion on the universality of the period-luminosity relation.
