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In this work we apply methods of Singularity Theory to study the Recognition Problem in Bifurcation Theory. We concentrate in bifurcation problems (h(x, λ) in the ring E_n+1 of germs of functions of n state variables and one parameter. Higher-order terms O _a(h), are caracterized by an intrinsic ideal P(h) contained in O_a(h). The main result shows that itr(M.RT(h) ⊂ P(h), characterizing P(h) in an effectively computable way. When n = 1 we show that P(h) = itr J(h).