Gagliardi et al. (1996, unpublished manuscript) defined an irregular multigraph to be a loopless multigraph with degree sequence n, n - 1,..., 1, and they posed the problem of determining the number of different irregular multigraphs f n on n vertices. In Gagliardi et al. (1996) they showed that if n = 0 or 3 (mod 4) then f n > n - 1. In this note our aim is to show that there are constants 1 < c 1 < c 2 and n 0 > 0 such that if n >= n 0 and n = 0 or 3 (mod 4) then (c 1 ) n 2 < f n < (c 2 ) n 2 . Indeed, we show that c 1 = 1.19 and c 2 = 1.65 can be chosen.