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Thank you, this worked out perfectly!

Hi,

you could use the decorations.markings library and he mark decoration option, as described in Section 27.6 "Mark Decorations: Adding Arrow Tips and Nodes on a Path" of the pgfmanual (p. 267ff); a little example:

\documentclass{book}
\usepackage{tikz ...

I am trying to draw a phase portrait for a system of ODEs, and would like several arrow tips along each curve to indicate direction.

So far, the closest I have come up with is to draw each curve twice, once in the usual way and once using the "triangles" path decoration to approximate an arrow tip ...