A generalisation of our previous approach of a renormalon-motivated resummation of the QCD observables is presented. Previously, it was constructed for those spacelike observables whose perturbation expansion is ${\cal D}(Q^2) = a(Q^2) + {\cal O}(a^2)$, where $a(Q^2) \equiv \alpha_s(Q^2)/\pi$ is the running QCD coupling. Now the resummation is generalised to spacelike quantities ${\cal D}(Q^2) = a(Q^2)^{\nu_0} + {\cal O}(a^{\nu_0+1})$ and timelike quantities ${\cal F}(\sigma) = a(\sigma)^{\nu_0} + {\cal O}(a^{\nu_0+1})$, where $\nu_0$ is in general a noninteger number ($0<\nu_0 \leq 1$). With this method, a timelike quantity is evaluated, namely the scheme-invariant factor of the Wilson coefficient of the chromomagnetic operator in the heavy-quark effective Lagrangian, and related quantities.