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The spectral evolution and spectral lag behavior of 92 bright pulses from 84gamma-ray bursts (GRBs) observed by the Fermi GBM telescope are studied. Thesepulses can be classified into hard-to-soft pulses (H2S, 64/92),H2S-dominated-tracking pulses (21/92), and other tracking pulses (7/92). Wefocus on the relationship between spectral evolution and spectral lags of H2Sand H2S-dominated-tracking pulses. %in hard-to-soft pulses (H2S, 64/92) andH2S-dominating-tracking (21/92) pulses. The main trend of spectral evolution(lag behavior) is estimated with $\log E_p\propto k_E\log(t+t_0)$(${\hat{\tau}} \propto k_{\hat{\tau}}\log E$), where $E_p$ is the peak photonenergy in the radiation spectrum, $t+t_0$ is the observer time relative to thebeginning of pulse $-t_0$, and ${\hat{\tau}}$ is the spectral lag of photonswith energy $E$ with respect to the energy band $8$-$25$ keV. For H2S andH2S-dominated-tracking pulses, a weak correlation between $k_{{\hat{\tau}}}/W$and $k_E$ is found, where $W$ is the pulse width. We also study the spectrallag behavior with peak time $t_{\rm p_E}$ of pulses for 30 well-shaped pulsesand estimate the main trend of the spectral lag behavior with $\log t_{\rmp_E}\propto k_{t_p}\log E$. It is found that $k_{t_p}$ is correlated with$k_E$. We perform simulations under a phenomenological model of spectralevolution, and find that these correlations are reproduced. We then concludethat spectral lags are closely related to spectral evolution within the pulse.The most natural explanation of these observations is that the emission is fromthe electrons in the same fluid unit at an emission site moving away from thecentral engine, as expected in the models invoking magnetic dissipation in amoderately-high-$\sigma$ outflow.

A comprehensive analysis of Fermi Gamma-Ray Burst Data: IV. Spectral lag and Its Relation to Ep Evolution