We discuss logarithmic corrections to form factors of mesons built from heavy quarks. The reactions e/sup +/e/sup -/ ..-->.. etasub(c)..gamma.. and H ..-->.. J/psi..gamma.. are considered as an example. A novel feature as compared to the well-studied problem of the pion form factor is the existence of transitions between the quark-antiquark state canti c and the gluonic one. O(..cap alpha..sub(s)) corrections are calculated exactly. An infinite series of the leading logarithmic terms (..cap alpha..sub(s)ln(Q/sup 2//m/sup 2/sub(c)))sup(n) is summed up with the help of the operator technique. Apart from results already known for quark operators, we use some new results referring to gluon operator and their mixing with those made from quarks. Two alternative derivations of the multiplicatively renormalizable operators are given. The first one reduces to a direct computation of the mixing matrix and its diagonalization, the second is based on conformal symmetry considerations.