  We present a study of the old globular clusters (GC) using archival F606W and
F814W HST/ACS images of 19 Magellanic-type dwarf Irregular (dIrr) galaxies
found in nearby (2 - 8 Mpc) associations of only dwarf galaxies. All dIrrs have
absolute magnitudes fainter than or equal to the SMC (Mv = -16.2 mag). We
detect 50 GC candidates in 13 dIrrs, of which 37 have (V-I) colors consistent
with "blue" (old, metal-poor) GCs (bGC). The luminosity function (LF) of the
bGCs in our sample peaks at Mv = -7.41 +/- 0.22 mag, consistent with other
galaxy types. The width of the LF is sigma = 1.79 +/- 0.31 which is typical for
dIrrs, but broader than the typical width in massive galaxies. The half-light
radii and ellipticities of the GCs in our sample (rh ~ 3.3 pc, e ~ 0.1) are
similar to those of old GCs in the Magellanic Clouds and to those of "Old Halo"
(OH) GCs in our Galaxy, but not as extended and spherical as the Galactic
"Young Halo" (YH) GCs (rh ~ 7.7 pc, e ~ 0.06). The e distribution shows a
turnover rather than a power law as observed for the Galactic GCs. This might
suggest that GCs in dIrrs are kinematically young and not fully relaxed yet.
The present-day specific frequencies (SN) span a broad range: 0.3 < SN < 11.
Assuming a dissipationless age fading of the galaxy light, the SN values would
increase by a factor of ~ 2.5 to 16, comparable with values for early-type
dwarfs (dE/dSphs). A bright central GC candidate, similar to nuclear clusters
of dEs, is observed in one of our dIrrs: NGC 1959. This nuclear GC has
luminosity, color, and structural parameters similar to that of wCen and M54,
suggesting that the latter might have their origin in the central regions of
similar Galactic building blocks. A comparison between properties of bGCs and
Galactic YH GCs, suspected to have originated from similar dIrrs, is performed.
