alien use causes gratuitous GC

I'm developing a Lisp application that links to C code.  The general
organization is that the Lisp code builds a function that encodes a
system of ordinary differential equations.  This function is passed off
to C code that solves the system and returns values of the variables
over time.  I have this code up and running in Allegro, Clisp, and
CMUCL, but for some reason CMUCL exhibits some memory problems.

Specifically, calls to solve the system of equations lead to several
invocations of the garbage collector (presumably due to memory
management issues) to the extent that the code cannot complete within a
reasonable time.

Any ideas what could be causing this?  Is there something flaky about
callbacks from C into Lisp?

Will