Using spaceborne particle and gamma-ray detection and radio diagnostics we study solar energetic particle (SEP) production in the 1996 July 9 event. This event is associated with an impulsive soft X-ray flare (9:10 UT) and a coronal mass ejection (CME). In a global classification the event is considered as mixed-impulsive. A sequence of acceleration processes is identified, starting early in the flare impulsive phase and continuing throughout the period when the CME propagated up to several Rsolar above the photosphere: (1) Gamma-ray, hard X-ray and cm-wave emitting particles seen during the flare impulsive phase in the low corona had no counterpart at the Solar and Heliospheric Observatory (SoHO) spacecraft. (2) Electrons accelerated at a coronal shock wave were revealed by decimetric- to-metric type II radio emission and by simultaneous radio signatures of beams traveling to 1 AU. (3) Mildly relativistic (>=250 keV) electrons detected by SoHO did not correspond to these shock-accelerated populations, but to later mainly impulsive injection which was associated with radio brightenings over a large range of coronal altitudes. (4) Energetic protons detected by SoHO were accelerated during about 100 min after the flare impulsive phase with a gradually evolving production profile that bore some similarity with the time profile of broadband metric (type IV) emission. (5) While all other particle signatures decayed, a second period of interplanetary proton production took place >=2 hours after flare onset. The first, 100 min period of SEP acceleration, post-impulsive phase coronal acceleration, is definitely dominant in mildly relativistic electrons. Two acceleration periods nearly equally contribute to the production of ~ 20 MeV protons. However, the second period is more productive in low energy, ~ 1 MeV, protons. The timing of the SEP injections indicates that neither the impulsive flare acceleration in the low corona nor the interplanetary CME at >= 10 Rsolar are the main sources of the high-energy particles observed onboard SoHO. We suggest that various acceleration processes related to the reconfiguration of the corona in the course of the flare and CME lift-off contribute to the interacting and escaping particle populations, with different signatures at different energies and in different species.