Methods for realization of an immittance whose argument is nearly constant at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda \pi/2, |\lambda|</tex> < 1, over an extended frequency range, are discussed. In terms of the generalized complex frequency variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> , these immittances are proportional to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s^{\lambda}</tex> , and as such they are approximations of Riemann-Louville fractional operators. First, we present a method which is applicable only for the special case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|\lambda| = \frac{1}{2}</tex> . This is based on the continued fraction expansion (CFE) of the irrational driving-point function of a uniform distributed RC (U <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{RC}</tex> ) network; the results are compared with those of earlier workers using lattice networks and rational function approximations. Next we discuss two methods applicable for any value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda</tex> between -1 and +1. One is based on the CFE of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(1 + s^{\pm 1})\pm\lambda</tex> ; the two signs result in two different circuits which approximate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s^{-\lambda}</tex> at low and high frequencies, respectively. The other method uses elliptic functions and results in an equiripple approximation of the constant-argument characteristic. In each method, the extent of approximation obtained by using a certain number of elements is determined by use of a digital computer. The results are given in the form of curves of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_2/ \omega_1</tex> versus the number of elements, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_2</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_1</tex> , denote the upper and lower ends, respectively, of the frequency band over which the argument is constant to within a certain tolerance. From the lumped element networks, we derive some <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{RC}</tex> networks which can approximate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{\lambda}</tex> more effectively than the lumped networks. The distributed structures can be fabricated in microminiature form using thin-film techniques, and should be more attractive from considerations of cost, size, and reliability.