Using a unified representation for the two current-feedback operational-amplifiers (CFOAs) based sinusoidal oscillators, new structures and circuits of this type are systematically discovered. Three catalogues for three different structures with each structure realizing 17 oscillator circuits are presented. Some of the new circuits are enjoying the attractive features of using grounded capacitors and/or independent/orthogonal tuning for the frequency and condition of oscillation. However, the classification of independent/orthogonal tuning may be misleading as it is based on using the Barkhausen criterion. Therefore, it is shown that using the roots of the characteristic equation of a specific oscillator circuit; while not leading to accurate results, may avoid any misleading conclusion regarding the orthogonal tuning of the frequency and condition of oscillation. Experimental results using the AD844 CFOA are included.