This paper examines the time-varying interactive linkages between the sustainable debt market and gas markets, applying unique estimation techniques, specifically the empirical mode decomposition (EMD)-windowed-cross-correlation (EMD-WCC) and wavelet-windowed-cross-correlations. To this end, we use the S&P Green Bond Index as a representative of a sustainable debt market while for the gas market, we use natural gas price indices of UK NBP (National Balancing Point), NYMEX HH (Henry Hub) and US shale gas prices. The lead/lag behavior amid green-bonds along with shale gas, also with natural gas markets has equal forces across all time scales. There exists weak cross-correlation across green bonds and shale gas markets and additionally, green bonds and natural gas markets in the short-run. Such findings imply that, from the perspective of the investors, in the short-run, green bonds have ample diversification benefits. The highest intensity of cross-correlations is observed in the longer time horizons. This evidence suggests that in the long-run the behavior of the markets is driven by its own peculiarities. Overall, our findings support the argument that green bonds with their climate-friendly properties add to the diversification benefits for investors, as a newer class of asset for portfolio investments.