For all convolution algebras L1[0; 1); L1 loc and A(!) = T n L1(!n), the derivations are of the form Dμf = Xf μ for suitable measures μ, where (Xf)(t) = tf(t). We describe the (weakly) compact as well as the (weakly) Montel derivations on these algebras in terms of properties of the measure μ. Moreover, for all these algebras we show
that the extension of Dμ to a natural dual space is weak-star continuous.