  Magnetic monopoles are known to emerge as leading non-perturbative
fluctuations in the lattice version of non-Abelian gauge theories in some
gauges. In terms of the Dirac quantization condition, these monopoles have
magnetic charge |Q_M|=2. Also, magnetic monopoles with |Q_M|=1 can be
introduced on the lattice via the 't Hooft loop operator. We consider the
|Q_M|=1,2 monopoles in the continuum limit of the lattice gauge theories. To
substitute for the Dirac strings which cost no action on the lattice, we allow
for singular gauge potentials which are absent in the standard continuum
version. Once the Dirac strings are allowed, it turns possible to find a
solution with zero action for a monopole--antimonopole pair. This implies
equivalence of the standard and modified continuum versions in perturbation
theory. To imitate the nonperturbative vacuum, we introduce then a nonsingular
background. The modified continuum version of the gluodynamics allows in this
case for monopoles with finite non-vanishing action. Using similar techniques,
we construct the 't Hooft loop operator in the continuum and predict its
behavior at small and large distances both at zero and high temperatures.
