  In the present paper, we consider timelike general rotational surfaces in the
Minkowski 4-space which are analogous to the general rotational surfaces in the
Euclidean 4-space introduced by C. Moore. We study two types of such surfaces
(with timelike and spacelike meridian curve, respectively) and describe
analytically some of their basic geometric classes: flat timelike general
rotational surfaces, timelike general rotational surfaces with flat normal
connection, and timelike general rotational surfaces with non-zero constant
mean curvature. We give explicitly all minimal timelike general rotational
surfaces and all timelike general rotational surfaces with parallel normalized
mean curvature vector field.
