Résumé
For every alpha <= beta in a left neighborhood [alpha(0), 1] of 1, a group G (alpha, beta) is constructed, the growth function of which satisfies lim inf log log b(G(alpha, beta)) (r)/log r = alpha and lim sup log log b(G(alpha, beta)) (r)/log r = beta. When alpha = beta, this provides an explicit uncountable collection of groups with growth functions strictly comparable. On the other hand, oscillation in the case alpha < beta explains the existence of groups with non comparable growth functions. Some period exponents associated to the frequency of oscillation provide new group invariants.