This paper is devoted to the study of normal form transformations and resonances. The usual theory of normal forms is formulated in a more general context: the quasi-monomial formalism, in which negative and non-integer exponents are accepted. The general coefficient of the Poincaréseries is explicitly constructed in the non-resonant case, for any QM system. From there arises the necessity to generalize resonances to non-analytical vector fields. Using particular changes of parameterization, we extend this resonance relation to the nonlinear part of the vector field. The changes of variables that arise from this provide approximations of the solutions far from the fixed point.