In this paper, we study two one-parameter families of random band Toeplitz matrices: [Formula: see text] where (1) a0 = 0, {a1, a2, …} in An(t) are independent random variables and a-i = ai; (2) a0(t) = 0, {a1(t), a2(t), …} in Bn(t) are independent copies of the standard Brownian motion at time t and a-i(t) = ai(t). As t varies, the empirical measures μ(An(t)) and μ(Bn(t)) are measure valued stochastic processes. The purpose of this paper is to study the fluctuations of μ(An(t)) and μ(Bn(t)) as n goes to ∞. Given a monomial f(x) = xp with p ≥ 2, the corresponding rescaled fluctuations of μ(An(t)) and μ(Bn(t)) are [Formula: see text] respectively. We will prove that the above equations converge to centered Gaussian families {Zp(t)} and {Wp(t)} respectively. The covariance structure 𝔼[Zp(t1)Zq(t2)] and 𝔼[Wp(t1)Wq(t2)] are obtained for all p, q ≥ 2, t1, t2 ≥ 0, and are both homogeneous polynomials of t1 and t2 for fixed p, q. In particular, Z2(t) is the Brownian motion and Z3(t) is the same as W2(t) up to a constant. The main method of this paper is the moment method.