Laser dynamics of a 10 GHz 0.55 ps asynchronously harmonic modelocked Er-doped fiber soliton laser are investigated both theoretically and experimentally. Theoretical analyses based on the master equation model solved by the variational method have indicated that all the pulse parameters of the laser output will exhibit complicated slow periodic variations in the asynchronous soliton modelocking (ASM) mode. New experimental methods based on analyzing directly the RF spectra of the ASM laser output have been developed to accurately determine the sinusoidal variation of the pulse timing and the pulse center wavelength for the first time. It is found that the pulse center wavelength variation can be as large as 1 nm half-peak-to-peak and the pulse timing variation can be as large as 3 ps. The consistency among all the experimental data and theoretical prediction is carefully examined and the results indicate that the ASM pulse dynamics observed experimentally are in good agreement with those obtained from the theoretical analyses.