Key words Ordinary differential equations, parameter dependence MSC (2010) 34A12, 34A34, 34A36 The paper studies differential equations of the form u (x) = f (x, u(x), λ(x)), u(x0 ) = u0 , where the righthand side is merely measurable in x. In particular sufficient conditions for the continuous and the differentiable dependence of solution u on the data and on the parameter λ are stated.