The author deals with the initial-boundary value problem on a half-line for the Kuramoto-Sivashinsky-type equations \[ \begin{aligned} u_t+ N(u,u_x)+ Ku&= 0,\quad t> 0,\;x> 0,\\ u(x,0)= u_0(x),\;x> 0,\;\partial^{j-1}_x u(0,t)&= 0,\quad t> 0,\;j=1,2.\end{aligned}\tag{1} \] The linear part of (1) is a differential operator \(Ku= -\partial^2_x+ \partial^4_x\) and the nonlinearity \(N(u,u_x)\) is of nonconvective type and satisfies the estimate \[ |N(u,v)|\leq C|u|^\rho|v|^\sigma\tag{2} \] with \(\rho\), \(\sigma\geq 0\). The main goal of the author is to prove global existence of solution for (1) and to study large-time behaviour of solutions to the (1) in the subcritical case, when the time decay rate of the nonlinearity in (1) is less than that of the linear terms (therefore the nonlinearity defines the asymptotic profile of solutions).