  We present an investigation of the globular cluster (GC) systems of NGC 3607
and NGC 3608 as part of the ongoing SLUGGS survey. We use wide-field imaging
data from the Subaru telescope in the g, r, and i filters to analyse the radial
density, colour and azimuthal distributions of both GC systems. With the
complementary kinematic data obtained from the Keck II telescope, we measure
the radial velocities of a total of 81 GCs.
  Our results show that the GC systems of NGC 3607 and NGC 3608 have a
detectable spatial extent of ~ 15, and 13 galaxy effective radii, respectively.
Both GC systems show a clear bimodal colour distribution. We detect a
significant radial colour gradient for the GC subpopulations in both galaxies.
NGC 3607 exhibits an overabundance of red GCs on the galaxy minor axis and NGC
3608 shows a misalignment in the GC subpopulation position angles with respect
to the galaxy stellar component.
  With the aid of literature data, we discuss several relationships between the
properties of GC systems and their host galaxies. A one-to-one relation between
the ellipticities of red GCs and the galaxy stellar light emphasises the
evolutionary similarities between them. In our sample of four slowly rotating
galaxies with kinematically decoupled cores, we observe a higher ellipticity
for the blue GC subpopulation than their red counterparts. Also, we notice the
flattening of negative colour gradients for the blue GC subpopulations with
increasing galaxy stellar mass. Finally, we discuss the formation scenarios
associated with the blue GC subpopulation.
