  We prove Malgrange's conjecture on the absence of confluence phenomena for
integrable meromorphic connections. More precisely, if $ Y\to X$ is a
complex-analytic fibration by smooth curves, $Z$ a hypersurface of $Y$ finite
over $X$, and $\nabla$ an integrable meromorphic connection on $Y$ with poles
along $Z$, then the function which attaches to {\smit x} $\in X$ the sum of the
irregularities of the fiber $\nabla_{(x)}$ at the points of $Z_x$ is lower
semicontinuous.
  The proof relies upon a study of the formal structure of integrable
meromorphic connections in several variables.
