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In der vorliegenden Arbeit untersuchen wir die Verteilung der Nullstellen Dirichletscher L-Reihen auf oder in der Nähe der kritischen Geraden. Diese Funktionen und ihre Nullstellen stehen im Mittelpunkt des Interesses bei einer Vielzahl klassischer zahlentheoretischer Fragestellungen; beispielsweise besagt die Verallgemeinerte Riemannsche Vermutung, daß sämtliche Nullstellen dieser Funktionen auf der kritischen Geraden liegen. Unsere Ergebnisse gehen unter anderem über die besten bislang bekannten Abschätzungen - für den Anteil der Nullstellen der Dirichletschen L-Reihen, die auf der kritischen Geraden liegen, - für den Anteil einfacher beziehungsweise m-facher Nullstellen sowie - über Nullstellen in der Nähe der kritischen Geraden hinaus. Wir setzen hiermit Arbeiten von A. Selberg, N. Levinson, J. B. Conrey und anderen fort und verallgemeinern Ergebnisse, die für die Riemannsche #-Funktion gültig sind, auf alle Dirichletschen LReihen beziehungsweise verbessern bisherige Resultate. Nach einer ausführlicheren Darstellung der Hintergründe zeigen wir einen Satz über Mittelwerte "geglätteter" L-Reihen, d.h. mit einem geeigneten Dirichlet-Polynom multiplizierte L-Reihen. Solche Mittelwertsätze stellen ein wesentliches Hilfsmittel zur Untersuchung der Nullstellenverteilung dar. Die in unserem Hauptsatz gegebene asymptotische Darstellung dieses Mittelwertes können wir dann nutzen, um die genannten Ergebnisse herzuleiten.