  The correlation between instantons and QCD-monopoles is studied both in the
lattice gauge theory and in the continuum theory. From a simple topological
consideration, instantons are expected to live only around the QCD-monopole
trajectory in the abelian gauge. First, the instanton solution is analytically
studied in the Polyakov-like gauge, where $A_4(x)$ is diagonalized. The world
line of the QCD-monopole is found to be penetrate the center of each instanton
inevitably. For the single-instanton solution, the QCD-monopole trajectory
becomes a simple straight line. On the other hand, in the multi-instanton
system, the QCD-monopole trajectory often has complicated topology including a
loop or a folded structure, and is unstable against a small fluctuation of the
location and the size of instantons. We also study the thermal instanton system
in the Polyakov-like gauge. At the high-temperature limit, the monopole
trajectory becomes straight lines in the temporal direction. The topology of
the QCD-monopole trajectory is drastically changed at a high temperature.
Second, the correlation between instantons and QCD-monopoles is studied in the
maximally abelian (MA) gauge and/or the Polyakov gauge using the SU(2) lattice
with $16^4$. The abelian link variable $u_\mu (s)$ is decomposed into the
singular (monopole-dominating) part $u_\mu ^{Ds}(s)$ and the regular
(photon-dominating) part $u_\mu ^{Ph}(s)$. The instanton numbers, $Q({\rm Ds})$
and $Q({\rm Ph})$, are measured using the SU(2) variables, $U_\mu ^{Ds}(s)$ and
$U_\mu ^{Ph}(s)$, which are reconstructed by multiplying the off-diagonal
matter factor to $u_\mu ^{Ds}(s)$ and $u_\mu ^{Ph}(s)$, respectively. A strong
correlation is found between $Q({\rm Ds})$ in the singular part and the
ordinary topological charge $Q({\rm SU(2)})$ even after the Cabibbo-Marinari
