<p>Dual-wavelength mode-locked fiber lasers unlock a range of significant dual-comb-based applications. However, rare studies describe dissipative soliton buildup dynamics from them. Here, we report the real-time observation of the buildup processes of stationary and pulsating asynchronous dual-wavelength dissipative solitons in a net-normal-dispersion Er-doped fiber laser. The 1557 nm dissipative soliton forms through relaxation oscillation, while the 1530 nm dissipative soliton evolves from transient Q-switching mode-locked pulse bursts, which also lead to the transient spectrum oscillation in the 1557 nm waveband. At the same pump power and polarization-controller (PC) setting, both the formation process of stationary and pulsating dual-wavelength dissipative solitons can be observed. External disturbances to the non-polarization-maintaining laser cavity may result in a slight change in unsaturated loss, contributing to the formation of the pulsating solitons, as indicated by our numerical simulations. Our findings provide insight into the complex buildup dynamics of dual-wavelength dissipative solitons and might benefit the laser design and their forward application.</p>