Derivational time and space complexity of context-free grammars is studied. Minimal linear bounds are given for the number of derivation steps needed to derive a word (time complexity) and for the length of the longest sentential form needed in the derivation of a word (space complexity). Coefficients in linear estimations are grammar dependent, for \(\epsilon\)-free grammars they depend on the number of nonterminals and in the case of arbitrary grammars they depend moreover on the number of nullable nonterminals and the length of the longest production. Examples are given to prove the minimality of the given bounds.