  We consider the compact space of pairs of nested partitions of $\mathbb N$,
where by analogy with models used in molecular evolution, we call "gene
partition" the finer partition and "species partition" the coarser one. We
introduce the class of nondecreasing processes valued in nested partitions,
assumed Markovian and with exchangeable semigroup. These processes are said
simple when each partition only undergoes one coalescence event at a time (but
possibly the same time). Simple nested exchangeable coalescent (SNEC) processes
can be seen as the extension of $\Lambda$-coalescents to nested partitions. We
characterize the law of SNEC processes as follows. In the absence of gene
coalescences, species blocks undergo $\Lambda$-coalescent type events and in
the absence of species coalescences, gene blocks lying in the same species
block undergo i.i.d. $\Lambda$-coalescents. Simultaneous coalescence of the
gene and species partitions are governed by an intensity measure $\nu_s$ on
$(0,1]\times {\mathcal M}_1 ([0,1])$ providing the frequency of species merging
and the law in which are drawn (independently) the frequencies of genes merging
in each coalescing species block. As an application, we also study the
conditions under which a SNEC process comes down from infinity.
