The author considers the Lyapunov approach to integrodifferential equations of the type \[ x'(t)+A(t)x(t)=\int^{t}_{t_ 0}C(t,s)x(s)ds+f(t),\quad t\geq t_ 0,\quad x(t_ 0)=x_ 0, \] and \(d/dt(x(t)+\int^{t}_{t_ 0}G(t,s)x(s)ds+g(t))+A(t)x(t)=0\), \(t\geq t_ 0\), \(x(t_ 0)=x_ 0\). The main point of the paper is that it is possible to use a simple Lyapunov function, typically some norm of the solution raised to some power. Such Lyapunov functions are not decreasing along solutions, so much more effort has to be put into proving that the solutions are bounded (or has some other specified asymptotic behaviour). The emphasis of the paper is not on proving new results but rather on presenting a direct and straightforward technique for studying these problems. Although the equations investigated are linear, the results can easily be extended to nonlinear ones. The paper has been inspired by a number of papers by T. A. Buron (and co-workers) where the approach has been to use more complicated Lyapunov functions.