  The (parallel) linear transports along paths in vector bundles are
axiomatically described. Their general form and certain properties are found.
It is shown that these transports are locally (i.e. along every fixed path)
always Euclidean ones in a senses that there exist frames in which their
matrices are unit. The investigated transports along paths are described in
terms of their local coefficients, as well as in terms of derivations along
paths.
