We study the motions of a spring pendulum as a function of its two con
trol parameters (the ratio of the spring and pendulum frequencies, and
the energy). It is shown that in the limits for very small and very l
arge parameter values the dynamics of the spring pendulum is predomina
ntly regular, while at intermediate parameter values the majority of i
nitial conditions lead to chaotic trajectories. Thus, upon varying the
parameters from small to large values one typically witnesses a trans
ition from order to chaos and back to order again. Similar order-chaos
-order sequences are observed in many other dynamical systems, and the
spring pendulum is a representative example. In this context, we also
discuss the phenomenon for which the spring pendulum is famous, namel
y the to-and-fro transfer between spring- and pendulum-like behaviour
when the spring frequency is (approximately) twice the pendulum freque
ncy. This turns out to play an important role in the order-chaos-order
sequence.