Digital elevation models (DEM) are of fundamental importance for remote sensing. With a DEM the three-dimensional positioning, requiring a stereo model can be reduced to a two-dimensional solution just based on a single image. With the free of charge availability of the SRTM-height models, covering the land area from 56 degrees southern up to 60.25 degrees northern latitude a nearly world wide coverage is given. But especially in mountainous regions and dry sand deserts the original SRTM DEMs have gaps in the original SRTM data. Now with the also free of charge available ASTER GDEM the area from 83 degrees southern up to 83 degrees northern latitude is covered. For areas where both height models exist, it is the question which height model should be preferred. Outside the USA the SRTM height data have a spacing of 3 arcsec (nearly 90m), while the ASTER GDEM has a spacing of just 1 arcsec (nearly 30m). The decision for the selection of the DEM is based on accuracy, homogeneity, reliability, completeness and morphologic details. In test areas with precise reference height models, located in the USA, Germany, France, Poland, Turkey and Jordan and with different morphology as mountainous, rolling, flat and urban and also with different land classes, the ASTER GDEM has been analyzed and compared with SRTM DEM as well as with SPOT 5 HRS and Cartosat 1 height models. ASTER GDEM in most cases shows improved accuracy with a higher number of number of stacks (number of images used for overlapping height models). But the accuracy improvement with more stacks is smaller as it should be for random data. The number of used stacks per DEM-point varies strongly depending upon the area. Especially in areas with low cloud coverage and higher imaging priority a high number of stacks have been used opposite to areas often covered by clouds and having lower imaging priority, where the dominating number of DEM-points may be located only in 2 stacks. Based on own matching results with ASTER images quite more morphologic details have been expected in ASTER GDEM having 1 arcsec point spacing as in SRTM height models with 3 arcsec spacing, but the analyzed data show only slightly more morphologic details as the SRTM 3" height model. SRTM as well as ASTER height models are strongly depending upon the morphology and the land coverage, so not a homogenous accuracy can be expected. In addition, as all height models, the accuracy depends usually linear upon the tangent of terrain slope, so the standard deviation of height (SZ) should be given in the form SZ = a + b*tan(terrain slope). Not only the standard deviation is important, the height models have different systematic errors (bias). The bias in X, Y and Z is larger for ASTER GDEM as for SRTM DEMs. Horizontal shifts have been determined by adjustment of the ASTER GDEMs against the reference height model. In general the SRTM height models are slightly more accurate as the ASTER GDEM.