Total columns measured with the ground-based solar FTIR technique are highly variable in time due to atmospheric chemistry and dynamics in the atmosphere above the measurement station. In this paper, a multiple regression model with anomalies of air pressure, total columns of hydrogen fluoride (HF) and carbon monoxide (CO) and tropopause height are used to reduce the variability in the methane (CH4) and nitrous oxide (N2O) total columns to estimate reliable linear trends with as small uncertainties as possible. The method is developed at the Harestua station (60°N, 11°E, 600ma.s.l.) and used on three other European FTIR stations, i.e. Jungfraujoch (47°N, 8°E, 3600ma.s.l.), Zugspitze (47°N, 11°E, 3000ma.s.l.), and Kiruna (68°N, 20°E, 400ma.s.l.). Linear CH4 trends between 0.13±0.01-0.25±0.02%yr−1 were estimated for all stations in the 1996-2009 period. A piecewise model with three separate linear trends, connected at change points, was used to estimate the short term fluctuations in the CH4 total columns. This model shows a growth in 1996–1999 followed by a period of steady state until 2007. From 2007 until 2009 the atmospheric CH4 amount increases between 0.57±0.22–1.15±0.17%yr−1. ... mehrLinear N2O trends between 0.19±0.01–0.40±0.02%yr−1 were estimated for all stations in the 1996-2007 period, here with the strongest trend at Harestua and Kiruna and the lowest at the Alp stations. From the N2O total columns crude tropospheric and stratospheric partial columns were derived, indicating that the observed difference in the N2O trends between the FTIR sites is of stratospheric origin. This agrees well with the N2O measurements by the SMR instrument onboard the Odin satellite showing the highest trends at Harestua, 0.98±0.28%yr−1, and considerably smaller trends at lower latitudes, 0.27±0.25%yr−1. The multiple regression model was compared with two other trend methods, the ordinary linear regression and a Bootstrap algorithm. The multiple regression model estimated CH4 and N2O trends that differed up to 31% compared to the other two methods and had uncertainties that were up to 300% lower. Since the multiple regression method were carefully validated this stresses the importance to account for variability in the total columns when estimating trend from solar FTIR data.