A comprehensive study of the correlation between various structural (Delta omega degrees, c-axis), electrical (T-c, Delta T) and linear microwave properties (R-S (T-0), lambda(T-0) and sigma(I) (T-0)) of epitaxial YBCO thin films on MgO and LaAlO3 substrates, and also their nonlinear microwave properties (H-rf(*) dR(s)/dHrf, H-rf-TOI(2), m-slope and H-rf-30dB(2)) has been performed. It was found that among the numerous parameters from the first group, the nonlinear microwave properties appear to correlate well only with the low-temperature penetration depth lambda(T-0), residual quasiparticle conductivity sigma(1) (T-0) and the c-axis lattice parameter. Here, among those three parameters the best correlation of the nonlinear properties is observed with lambda (T-0). The correlation of the other parameters from the first group with the nonlinear microwave performance of the films is either not evident, because of the wide spread of the data, or absent. There is also seen a correlation within the group of linear microwave parameters (such as R-s (T-0), sigma(1) (T-0) and lambda (T-0)) and partial correlation within the group of the nonlinear parameters (such as H-rf(*), dR(s)/dH(rf) and H-rf-TOI(2)). However, all the aforementioned correlations seem to be dependent on many conditions (such as film growth technique and substrate), and are by no means quantitative, but only qualitative.