  In this paper we study unfoldings of saddle-nodes and their Dulac time. By
unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem
A) we prove uniform regularity by which orbits and their derivatives arrive at
a node. Uniformity is with respect to all parameters including the unfolding
parameter bringing the node to a saddle-node and a parameter belonging to a
space of functions. In the second part, we apply this first result for proving
a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an
unfolding of a saddle-node. This result is a building block in the study of
bifurcations of critical periods in a neighbourhood of a polycycle. Finally, we
apply Theorems A and B to the study of critical periods of the Loud family of
quadratic centers and we prove that no bifurcation occurs for certain values of
the parameters (Theorem C).
