The F-matrix expressions of inverted-L-type four-terminal networks, each involving an element with the power-law conductivity σ(ω)ωa (0a1) connected to a resistance R, an inductance L or a capacitance C, were derived using the standard procedures of Laplace transformation, indicating that the exponents of the complex angular frequency s, so far limited to the integers for the transmission circuits with finite elements, can be extended to the real numbers. The responses to a step voltage calculated show hysteretic behavior reflecting the resistance-capacitance ambivalent nature of the power-law conductivity.