  The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$
series are given in a convenient form, which allows their direct computation
and clarifies their connection with the $q=1$ case. These equations, defining
the field strengths, are essential in the construction of $q$-deformed gauge
theories. An explicit expression $\om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l$
for the $q$-commutations of left-invariant one-forms is found, with $\Z{ij}{kl}
\om^k \we \om^l \qonelim \om^j\we\om^i$.
