Gene expression is controlled by the combinatorial effects of regulatory factors from different biological subsystems such as general transcription factors (TFs), cellular growth factors and microRNAs. A subsystem's gene expression may be controlled by its internal regulatory factors, exclusively, or by external subsystems, or by both. It is thus useful to distinguish the degree to which a subsystem is regulated internally or externally-e.g., how non-conserved, species-specific TFs affect the expression of conserved, cross-species genes during evolution. We developed a computational method (DREISS, dreiss.gerteinlab.org) for analyzing the Dynamics of gene expression driven by Regulatory networks, both External and Internal based on State Space models. Given a subsystem, the "state" and "control" in the model refer to its own (internal) and another subsystem's (external) gene expression levels. The state at a given time is determined by the state and control at a previous time. Because typical time-series data do not have enough samples to fully estimate the model's parameters, DREISS uses dimensionality reduction, and identifies canonical temporal expression trajectories (e.g., degradation, growth and oscillation) representing the regulatory effects emanating from various subsystems. To demonstrate capabilities of DREISS, we study the regulatory effects of evolutionarily conserved vs. divergent TFs across distant species. In particular, we applied DREISS to the time-series gene expression datasets of C. elegans and D. melanogaster during their embryonic development. We analyzed the expression dynamics of the conserved, orthologous genes (orthologs), seeing the degree to which these can be accounted for by orthologous (internal) versus species-specific (external) TFs. We found that between two species, the orthologs have matched, internally driven expression patterns but very different externally driven ones. This is particularly true for genes with evolutionarily ancient functions (e.g. the ribosomal proteins), in contrast to those with more recently evolved functions (e.g., cell-cell communication). This suggests that despite striking morphological differences, some fundamental embryonic-developmental processes are still controlled by ancient regulatory systems.