Let $\mathcal {F}$ and $\mathcal G$ be two distinct singular holomorphic foliations on a compact complex surface $M$, in the same , that is $N_\mathcal {F}=N_\mathcal G$. In this case, we can define the pencil $\mathcal {P}=\mathcal {P}(\mathcal {F},\mathcal G)$ of foliations generated by $\mathcal {F}$ and $\mathcal G$. We can associate to a pencil $\mathcal {P}$ a meromorphic $2$-form $\Theta =\Theta (\mathcal {P})$, the form of curvature of the pencil, which is in fact the Chern curvature (cf . [Ch]). When $\Theta (\mathcal {P})\equiv 0$ we will say that the pencil is flat. In this paper we give some sufficient conditions for a pencil to be flat. (Theorem 2). We will see also how the flatness reflects in the pseudo-group of holonomy of the foliations of $\mathcal {P}$. In particular, we will study the set $\lbrace \mathcal {H}\in \mathcal {P}\mid \mathcal {H} \text { has a first integral}\rbrace $ in some cases (Theorem 1).