Stark has conjectured the existence of an element in the number field \(K\) whose absolute values at infinite primes provide the evaluation of first derivatives at \(s=0\) of \(L\)-functions for an abelian extension \(K/k\). We first prove this conjecture with some basic class field theory for the case of a tame multiquadratic extension \(K/k\). Then, after Shintani, we consider the case when \(k\) is real quadratic and \(K\) is quadratic over an absolutely abelian field. Using Stark’s work, we improve Shintani’s result by proving the conjecture as stated above. That these two cases held promise was suggested in a paper of Tate.