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It is known that internal climate variability (ICV) can influence trends seen in observations and individual model simulations over a period of decades. This makes it difficult to quantify the forced response to external forcing. Here we analyze two large ensembles of simulations from 1950 to 2100 by two fully-coupled climate models, namely the CESM1 and CanESM2, to quantify ICV's influences on estimated trends in annual surface air temperature (Tas) and precipitation (P) over different time periods. Results show that the observed trends since 1979 in global-mean Tas and P are within the spread of the CESM1-simulated trends while the CanESM2 overestimates the historical changes, likely due to its deficiencies in simulating historical non-CO2 forcing. Both models show considerable spreads in the Tas and P trends among the individual simulations, and the spreads decrease rapidly as the record length increases to about 40 (50) years for global-mean Tas (P). Because of ICV, local and regional P trends may remain statistically insignificant and differ greatly among individual model simulations over most of the globe until the later part of the twenty-first century even under a high emissions scenario, while local Tas trends since 1979 are already statistically significant over many low-latitude regions and are projected to become significant over most of the globe by the 2030s. The largest influences of ICV come from the Inter-decadal Pacific Oscillation and polar sea ice. In contrast to the realization-dependent ICV, the forced Tas response to external forcing has a temporal evolution that is similar over most of the globe (except its amplitude). For annual precipitation, however, the temporal evolution of the forced response is similar (opposite) to that of Tas over many mid-high latitude areas and the ITCZ (subtropical regions), but close to zero over the transition zones between the regions with positive and negative trends. The ICV in the transient climate change simulations is slightly larger than that in the control run for P (and other related variables such as water vapor), but similar for Tas. Thus, the ICV for P from a control run may need to be scaled up in detection and attribution analyses.