High-resolution projections of the future climate are required to assess climate change realistically at a regional scale. This is in particular important for climate change impact studies since global projections are much too coarse to represent local conditions adequately. A major concern is thereby the change of extreme values in a warming climate due to their severe impact on the natural environment, socio-economical systems and the human health. Regional climate models (RCMs) are, however, able to reproduce much of those local features. Current horizontal resolutions are about 18-25km, which is still too coarse to directly resolve small-scale processes such as deep-convection. For this reason, projections of a possible future climate were simulated in this study with the regional climate model COSMO-CLM at horizontal resolutions of 4.5km and 1.3km for the region of Saarland-Lorraine-Luxemburg and Rhineland-Palatinate for the first time. At a horizontal scale of about 1km deep-convection is treated explicitly, which is expected to improve particularly the simulation of convective summer precipitation and a better resolved orography is expected to improve near surface fields such as 2m temperature. These simulations were performed as 10-year long time-slice experiments for the present climate (1991"2000), the near future (2041"2050) and the end of the century (2091"2100). The climate change signals of the annual and seasonal means and the change of extremes are analysed with respect to precipitation and 2m temperature and a possible added value due to the increased resolution is investigated. To assess changes in extremes, extreme indices have been applied and 10- and 20-year return levels were estimated by "peak-over-threshold" models. Since it is generally known that model output of RCMs should not directly be used for climate change impact studies, the precipitation and temperature fields were bias-corrected with several quantile-matching methods. Among them is a new developed parametric method which includes an extension for extreme values and is hence expected to improve the correction. In addition, the impact of the bias-correction on the climate change signals and on the extreme value statistics was investigated. The results reveal a significant warming of the annual mean by about +1.7 -°C until 2041"2050 and +3.7 -°C until 2091"2100, but considerably stronger signals of up to +5 -°C in summer in the Rhine Valley. Furthermore, the daily variability increases by about +0.8 -°C in summer but decreases by about -0.8 -°C in winter. Consequently, hot extremes increase moderately until the mid of the century but strongly thereafter, in particular in the Rhine Valley. Cold extremes warm continuously in the complete domain in the next 100 years but strongest in mountainous areas. The change signals with regard to annual precipitation are of the order -±10% but not significant. Significant, however, are a predicted increase of +32% of the seasonal precipitation in autumn until 2041"2050 and a decrease of -28% in summer until 2091-2100. No significant changes were found for days with intensities > 20 mm/day, but the results indicate that extremes with return periods ≤2 years increase as well as the frequency and duration of dry periods. The bias-corrections amplified positive signals but dampened negative signals and considerably reduced the power of detection. Moreover, absolute values and frequencies of extremes were altered by the correction but change signals remained approximately constant. The new method outperformed other parametric methods, in particular with regard to extreme value correction and related extreme indices and return levels. Although the bias correction removed systematic errors, it should be treated as an additional layer of uncertainty in climate change studies. Finally, the increased resolution of 1.3km improved predominantly the representation of temperature fields and extremes in terms of spatial heterogeneity. The benefits for summer precipitation were not as clear due to a severe dry-bias in summer, but it could be shown that in principle the onset and intensity of convection improves. This work demonstrates that climate change will have severe impacts in this investigation area and that in particular extremes may change considerably. An increased resolution provides thereby an added value to the results. These findings encourage further investigations, for other variables as for example near-surface wind, which will be more feasible with growing computing resources. These analyses should, however, be repeated with longer time series, different RCMs and anthropogenic scenarios to determine the robustness and uncertainty of these results more extensively.