The results of magnetic susceptibility (χ), electrical resistivity (ρ), heat-capacity (C), and thermopower (S) measurements on CeCuAs ₂, forming in the ZrCuSi₂-type tetragonal structure, are reported. Our investigations reveal that Ce is trivalent and there is no clear evidence for long range magnetic ordering down to 45 mK. The ρ behavior is notable in the sense that (i) the temperature (T)-coefficient of ρ is negative in the entire range of measurement (45 mK to 300 K) with large values of ρ, while the S behavior is typical of metallic Kondo lattices, and (ii) ρ is proportional to T^-0.6 at low temperatures, without any influence on the exponent by the application of a magnetic field, which does not seem to classify this compound into hither-to-known non-Fermi liquid (NFL) systems. In contrast to the logarithmic increase known for NFL systems, C/T measured down to 0.5 K exhibits a fall below 2 K. The observed properties of this compound are unusual among Ce systems.