Let $f:X\rightarrow B$ be a well-behaved $T^{2}$-fibration, $b_{0}\in\Delta\subseteq B$, $b$ a nearby point, and $T:H_{1}(X_{b},{\bf Z})\rightarrow H_{1}(X_{b},{\bf Z})$ the monodromy transformation about a simple loop around $b_{0}$ based at $b$. Then there is a basis $e_{1},e_{2}$ of $H_{1}(X_{b},{\bf Z})$ in which $T=\pmatrix{1&1\cr 0&1}$, $\pmatrix{0&-1\cr 1&1\cr}$ or $\pmatrix{0&-1\cr 1&3\cr}$. In the first case, the singular fibre is of type $I_{1}$ (by which we mean the one-point compactification of $S^{1}\times{\bf R}$), while in the second and third cases the singular fibre is topologically an $S^{2}$.