  Recent observations have reported that some gas-rich dwarf irregular (dIrr)
galaxies appear to have spherical distributions in the outer underlying old and
intermediate-age stellar populations (e.g., NGC 6822). These observations imply
that some dIrr's have two distinct (or ``two-component'') structures, i.e.,
inner disky and outer spherical ones, though the number fraction of dIrr's with
such structures remains observationally unclear. We discuss how such two
distinct structures are formed during dIrr formation based on observations and
simulations. Our numerical simulations show that the remnants of mergers
between two gas-rich dIrr's with initially extended gas disks can have both
extended spheroids composed of older stellar populations and disks composed
mostly of gas and young stars. The simulated remnants with two distinct
structures can be still identified as dIrr's owing to the presence of
star-forming regions. The structural properties of outer spherical structures
in dIrr's formed from dIrr-dIrr merging depend on initial conditions of
merging, which suggests that outer structures in dIrr's can be diverse. We also
discuss other possible physical mechanisms for the formation of outer spherical
structures composed of older stars in dIrr's.
