  The Brasselet number of a function $f$ with nonisolated singularities
describes numerically the topological information of its generalized Milnor
fibre. In this work, using the Brasselet number, we present several formulas
for germs $f:(X, 0) \rightarrow (\mathbb{C}, 0)$ and $g : (X, 0)\rightarrow
(\mathbb{C}, 0)$ in the case where g has a one-dimensional critical locus. We
also give applications when f has isolated singularities and when it is a
generic linear form.
