This paper deals with a class
$$\mathcal{MAG}_{\vec{k}}$$
of pseudorandom bit generators – modified alternating
$$\vec{k}$$
–generators. This class is constructed similarly to the class
$$\mathcal{ASG}_{\vec{k}}$$
of alternating step generators. Three subclasses of
$$\mathcal{MAG}_{\vec{k}}$$
are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass
$$\mathcal{MAG}_{\vec{k}}^{max}$$
of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of
$$\mathcal{MAG}_{\vec{k}}$$
to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating
$$\vec{k}$$
–generators, designed especially to be more secure, are presented.