  In this paper, we establish the second Bogolyubov theorem and global
averaging principle for stochastic partial differential equations (in short,
SPDEs) with monotone coefficients. Firstly, we prove that there exists a unique
$L^{2}$-bounded solution to SPDEs with monotone coefficients and this bounded
solution is globally asymptotically stable in square-mean sense. Then we show
that the $L^{2}$-bounded solution possesses the same recurrent properties (e.g.
periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff
recurrent, Levitan almost periodic, etc.) in distribution sense as the
coefficients. Thirdly, we prove that the recurrent solution of the original
equation converges to the stationary solution of averaged equation under the
compact-open topology as the time scale goes to zero--in other words, there
exists a unique recurrent solution to the original equation in a neighborhood
of the stationary solution of averaged equation when the time scale is small.
Finally, we establish the global averaging principle in weak sense, i.e. we
show that the attractor of original system tends to that of the averaged
equation in probability measure space as the time scale goes to zero. For
illustration of our results, we give two applications, including stochastic
reaction diffusion equations and stochastic generalized porous media equations.
