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Given a random RNA secondary structure, $S$, we study RNA sequences havingfixed ratios of nuclotides that are compatible with $S$. We perform thisanalysis for RNA secondary structures subject to various base pairing rules andminimum arc- and stack-length restrictions. Our main result reads as follows:in the simplex of the nucleotide ratios there exists a convex region in which,in the limit of long sequences, a random structure a.a.s.~has compatiblesequence with these ratios and outside of which a.a.s.~a random structure hasno such compatible sequence. We localize this region for RNA secondarystructures subject to various base pairing rules and minimum arc- andstack-length restrictions. In particular, for {\bf GC}-sequences having a ratioof {\bf G} nucleotides smaller than $1/3$, a random RNA secondary structurewithout any minimum arc- and stack-length restrictions has a.a.s.~no suchcompatible sequence. For sequences having a ratio of {\bf G} nucleotides largerthan $1/3$, a random RNA secondary structure has a.a.s. such compatiblesequences. We discuss our results in the context of various families of RNAstructures.

RNA secondary structures having a compatible sequence of certain nucleotide ratios