  We construct five independent screening currents associated with the
$U_q(\widehat{sl(3)})$ quantum current algebra. The screening currents are
expressed as exponentials of the eight basic deformed bosonic fields that are
required in the quantum analogue of the Wakimoto realization of the current
algebra. Four of the screening currents are `simple', in that each one is given
as a single exponential field. The fifth is expressed as an infinite sum of
exponential fields. For reasons we discuss, we expect that the structure of the
screening currents for a general quantum affine algebra will be similar to the
$U_q(\widehat{sl(3)})$ case.
