  We modify the definition of Aldous' multiplicative coalescent process and
introduce the multiplicative coalescent with linear deletion (MCLD). A state of
this process is a square-summable decreasing sequence of cluster sizes. Pairs
of clusters merge with a rate equal to the product of their sizes and clusters
are deleted with a rate linearly proportional to their size. We prove that the
MCLD is a Feller process. This result is a key ingredient in the description of
scaling limits of the evolution of component sizes of the mean field frozen
percolation model and the so-called rigid representation of such scaling
limits.
