Variables determining the number of native and alien plants on arable land in Central Europe are identified. Species richness of 698 samples of weed floras recorded in the Czech Republic in plots of a standard size of 100 m2 in 1955–2000 was studied in relation to altitudinally based floristic region, soil type, type of cultivated crop, climatic variables, altitude, year of the record, crop cover and height, and human population density in the region. Vascular plant species were classified into native and alien, the latter divided in archaeophytes, introduced before AD 1500, and neophytes, introduced after this date. The use of minimal adequate models in the analysis of covariance allowed determination of the net effects of mutually correlated environmental variables. Models for particular species groups explained 33–48% of variation in species numbers and 27–51% in proportions; however, explanatory variables affected native species, archaeophytes, and neophytes differently. The number and proportion of neophytes increased in 1955–2000, whereas the number of native species and archaeophytes declined (in archaeophytes more slowly in the warm than in the moderate to cool altitudinal floristic region). In warm and dry regions and on dry soils, where most archaeophytes find optimum conditions, fewer native species are able to persist in weed communities than in colder and wetter regions. Archaeophytes respond like neophytes to some variables (climate, seasonal development of crop) and alternatively like native species to other variables (increasing agricultural intensification through time, human population density). Archaeophytes are common in old crops introduced with the beginning of agriculture (cereals), but are poorly represented in relatively recently introduced crops (rape, maize), where neophytes are most numerous. These patterns reflect the history of plant invasions in Central Europe. Neolithic agriculture, introduced from the Near East in the sixth millenium BC, brought archaeophytes with crops and, by creating intense and continuous propagule pressure and imposing new agricultural management, facilitated their invasion. By contrast, the crops introduced during the past five centuries and their specific agrotechnical management have supported spreading of other weed species, mainly invaders from overseas.