The annual and the monthly mean values of the land-surface air temperature anomalies from 1880–2011, over both hemispheres, are used to investigate the existence of long-range correlations in their temporal evolution. The analytical tool employed is the detrended fluctuation analysis, which eliminates the noise of the non-stationarities that characterize the land-surface air temperature anomalies in both hemispheres. The reliability of the results obtained from this tool (e.g., power-law scaling) is investigated, especially for large scales, by using error bounds statistics, the autocorrelation function (e.g., rejection of its exponential decay) and the method of local slopes (e.g., their constancy in a sufficient range). The main finding is that deviations of one sign of the land-surface air temperature anomalies in both hemispheres are generally followed by deviations with the same sign at different time intervals. In other words, the land-surface air temperature anomalies exhibit persistent behaviour, i.e., deviations tend to keep the same sign. Taking into account our earlier study, according to which the land and sea surface temperature anomalies exhibit scaling behaviour in the Northern and Southern Hemisphere, we conclude that the difference between the scaling exponents mainly stems from the sea surface temperature, which exhibits a stronger memory in the Southern than in the Northern Hemisphere. Moreover, the variability of the scaling exponents of the annual mean values of the land-surface air temperature anomalies versus latitude shows an increasing trend from the low latitudes to polar regions, starting from the classical random walk (white noise) over the tropics. There is a gradual increase of the scaling exponent from low to high latitudes (which is stronger over the Southern Hemisphere).