  We study the properties of two classes of meromorphic functions in the
complex plane. The first one is the class of almost elliptic functions in the
sense of Sunyer-i-Balaguer. This is the class of meromorphic functions f such
that the family of shifts f(z+h) (h are complex numbers) is normal with respect
to the uniform convergence in the whole complex plane. Given two sequences of
complex numbers, we provide sufficient conditions for them to be zeros and
poles of some almost elliptic function. These conditions enable one to give
(for the first time) explicit non-trivial examples of almost elliptic
functions.
  The second class was introduced by K.Yosida, who called it a class of normal
functions of the first category. This is the class of meromorphic functions f
such that the family of shifts f(z+h)is normal with respect to the uniform
convergence on compacta in the complex plane and no limit point of the family
is a constant function. We give necessary and sufficient conditions for two
sequences of complex numbers to be zeros and poles of some normal function of
the first category and obtain a parametric representation for this class in
terms of zeros and poles.
