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In this paper we characterise the smoothness of the nested Quot scheme ofpoints of a smooth variety, namely the moduli space parametrising flags of$0$-dimensional quotients of a fixed locally free sheaf. Our results extendCheah's classification of smooth nested Hilbert schemes.  --  Dans cet article on caract\'erise la lissit\'e du sch\'ema Quot ponctuelembo\^it\'e d'une vari\'et\'e lisse, c'est-\`a-dire l'espace de modulesparam\'etrant les drapeaux de quotients de dimension $0$ d'un faisceaulocalement libre fix\'e. Nos r\'esultats \'etendent la classification de Cheahconcernant les sch\'emas de Hilbert ponctuels embo\^it\'es.

Sur la lissit\'e du sch\'ema Quot ponctuel embo\^it\'e